Do the lyrics (so far) describe a single coherent plot (a la rock operas such as The Wall), or are they more generically motivic/thematic?
There does not appear to be a single linear narrative.
This essay by Phil Sandifer gives a sort of critical overview of Monáe's work and the Metropolis saga. (All quotes throughout this answer are excerpted from Sandifer's essay.)
Nothing so straightforward as a plot summary is given, however, and Sandifer comments,
"by the end of the fifth track [of Suite 1], “Sincerely, Jane,” the notion of what a narrative is within the context of the Metropolis Saga becomes complex, to say the least."
Sandifer comments elsewhere that it is a "challenge" to "construct a linear narrative." This is fitting, because the plot is not, in fact, the point:
Much of the Metropolis Saga, after all, [demands] that we read things as code, taking the oppression of androids in Monáe’s imagined future as a metaphor for present-day oppressions.
Nevertheless, bits of plot can be strung together somewhat.
Suite I: The Chase
As expected, The Chase is about a chase. Specifically, the central character of the Metropolis saga, Cindi Mayweather, Monáe's alter-ego, is on the run from bounty hunters because she has broken a law against human/android relationships:
“March of the Wolfmasters” [is] a spoken word piece in the form of an announcement that “Android No. 57821, otherwise known as Cindi Mayweather, has fallen desperately in love with a human named Anthony Greendown,” which means that bounty hunters are now free to hunt her.
The second track continues this plot from Cindi's perspective; however,
But it is the third track, “Many Moons,” that serves as the suite’s key song.... The video...features Cindi Mayweather as a singing and dancing entertainer at the annual Metropolis Android Auction, a setting that cannot be reconciled with the ostensible plots of “March of the Wolfmasters” and “Violet Stars Happy Hunting!” ....
The song and video [end] with Cindi falling to the ground, seemingly dead.... [But] in the video, Cindi is one of several androids portrayed by Monáe, all of whom lip sync the lyrics in unison. As Cindi dies, the bulk of the lyrics are voiced by one of her alter-egos, Lady Maestra, Master of the Show Droids, whose veiled footwomen surround the dying Cindi as though to bear her away. Meanwhile, the lyrics, about how “ when the world just treats you wrong / just come with me and I’ll take you home” and how “the old man dies and then a baby’s born” suggest a theme of rebirth.
Sandifer suggests that the "many moons" of the song and the video suggest the use of time travel as a narrative device to allow the existence of multiple Cindis in multiple worlds.
[The next song,] “Cybertronic Purgatory,” depicts a captured Cindi...[but] “Sincerely, Jane” clearly depicts the real world.... In “Cybertronic Purgatory” Cindi is captured and destroyed, but this only causes her to reincarnate in a new setting entirely.
Suite II: The ArchAndroid Tracks 1-11
Sandifer does not explain much of a narrative in Suite II, and he notes that according to the liner notes, “most of the story does not bear logical sense.” (This is a direct quote from the liner notes.) The liner notes also state that
Monáe is originally from the year 2719, where she was kidnapped, had her genetic code stolen and used to create Cindi Mayweather, and was then sent back in time.
Beyond that, Sandifer does identify thematic elements in Suite II:
“Dance or Die”... develops the specifics of Monáe’s vision of resistance and revolution, with dancing not just serving as a means of waiting for the ArchAndroid, but as an explicit form of resistance and, more to the point, of survival in a fallen and degrading world. (“It’s still a war in all the streets and yes freaks will dance or die.”) This theme carries through the next three tracks, “Faster,” “Locked Inside,” and “Sir Greendown,” each of which...depict[s] their narrators in positions of captivity and longing for some form of release.
“Dance or Die”, according to Sandifer, also describes an "overt" war, whereas "Cold War" a few tracks later describes
a cold war, free of literal violence, where the primary stakes are the maintenance of your own identity.
The video for following song, "Tightrope", introduces an entirely new setting into the suite:
It takes place in the Palace of the Dogs, which is described as an asylum where “dancing has long been forbidden for its subversive effects on the residents and its tendency to lead to illegal magical practices.”
The liner notes apparently also state that "Monáe herself is imprisoned in the asylum."
The final three songs
present characters who have taken the lessons of “Cold War” and “Tightrope” to heart and found internal lives offering some measure of freedom.
The first, “Oh, Maker,” is...a mournful ballad from Cindi to her vision of God, which, sensibly for an android, is instead the Maker.
"Mushrooms & Roses", which closes the suite, is about a club called "Mushrooms & Roses", “where all the lonely droids and lovers have their wildest dreams" (this is taken directly from the lyrics). The song also introduces "Mary, a cryptically defined figure of attraction within the Metropolis Saga."
Suite III: The ArchAndroid Tracks 12-18
There is not much discussion of plot for these tracks in Sandifer's essay. However, it contain
the last mentions of Anthony Greendown in the Metropolis Saga to date...“57821”...is clearly about him, beginning with a description of how “Early each morning he searched for her / til his feet become bloody and tired.”
Of course, it is in Suite III that Cindi Mayweather becomes the messianic ArchAndroid, and Sandifer suggests that
Cindi’s ascension to the role of ArchAndroid must also be understood as a turn away from the life depicted back in Suite I and towards an altogether broader perspective.
Suite IV: The Electric Lady Tracks 1-10
Sandifer states that "Monáe has suggested that [The Electric Lady] is in fact a prequel to The Chase."
Sandifer describes the suite as "a swaggering, confident run of songs that can easily be read as embodying Cindi’s revolutionary potential," though it appears that once again there's not much in terms of explicit plot elements.
The accompanying video [for "Q.U.E.E.N."] posits Monáe and the rest of the Wondaland Arts Society as famous rebels from history who have been captured in suspended animation by the oppressive future regime of Metropolis, but who are broken out by a bunch of rebels armed only with a record containing the single (described in the voiceover as “a musical weapons project,” and as a freedom movement disguised as a song).
There is also an interlude featuring
DJ Crash Crash[, who proclaims that] that “we’re tired of fires, quiet no riots, we are jamming, dancing, and loving. Don’t throw no rock, don’t break no glass, just shake your ass.”
The next song with an accompanying video is "PrimeTime":
[The video takes] place at the Electric Sheep Nightclub, a bar featuring seductively dancing androids. [It depicts] Cindi as a waitress at the nightclub flirting with a patron, Joey Vice...and finally storming out of the club after she’s harassed by a[nother] patron, culminating in a rooftop meeting with Joey Vice, who takes her to an underground club and subsequently to his apartment, where there are drinks, Chinese food, and seductive looks.
"Dance Apocalyptic" is explicitly one of Cindi's songs.
Suite V: The Electric Lady Tracks 11-19
The final suite (so far) is perhaps the least connected to the original science fiction plot of Suite I:
With the exception of its interlude...there are no sci-fi signifiers anywhere in Suite V.
"Ghetto Woman" appears partly autobiographical:
It is a hymn to a particular archetype of black femininity, one firmly rooted in urban poverty...[and is proclaimed] to be “the seventh wonder reigning over us at night” and...to be “built to last through any weather.” [The song's end is] overtly autobiographical for Monáe, describing her relationship with her own mother and including the lyric “before the tuxedos and black and white every day / used to watch my momma get down on her knees and pray / she’s the reason that I’m even writing this song."
The suite again features DJ Crash Crash, with
a trio viewpoints [callers] that are distinctly positioned as outside the oppressed android culture.
One of these callers explicitly mentions the ArchAndroid mythos:
...he asks “You know, if you guys, in android community truly believe that Cindi Mayweather is not just like the Electric Lady Number One and all, but like also the ArchAndroid? Because of course in the book of...” But more interesting is DJ Crash Crash’s response which is to hurriedly cut him off with a “no, no, not on my show” and hang up on him, an apparent rejection of the messianic vision of the previous album.
"Sally Ride" and "Dorothy Dandridge Eyes" don't appear to directly relate to prior Metropolis saga plot elements, but their names do refer to real-life historical figures:
Sally Ride [was] the first American woman in space, who died in 2012 during The Electric Lady’s production and posthumously came out as having been in a same-sex relationship.... Dorothy Dandridge [was] the first black actress to get a nomination for Best Actress at the Oscars.
Sandifer gives a fairly compelling summary of the saga as a whole:
Cindi Mayweather has always been about becoming - a transformation from dystopia to utopia that is always happening and thus never fully realized. As Monáe says to her alterego in [The Electric Lady]’s liner notes, “see you where I always see you, in the future.”