Your best bet in the classical world may well be Flemish Polyphony.
A bit of research indicates that the subgenre of late Burgundian motet is the ideal overlap of complex polyphony with a distinct lead voice:
I've found it difficult to find this elsewhere in classical chorale music, although that may well represent my limitations more than that of the form. Here are my best tries:
This spiritual is quite similar to a classical style, much like the Flemish Polyphony. It alternates solo sections with a harmonized, polyphonic version of the same line.
This song isn't classical, but it's from the European ballad tradition. It's not exactly lead-and-chorus, but there's a main line that overlaps a counterpoint part.
The transcendent harmonies on some of the Brian Wilson ballads is about as close as you get to classical chorale in pop music:
Barbershop is quite a bit like classical chorale, with some added African-American influences. It doesn't typically have a strong lead, but here's a notable exception where the lead voice is a different song being sung over the backing chorus (the two songs combine around 3:19). I feel that might be a productive model to follow (composing the lead and the backing vocals semi-independently). That's a trick used fairly often on Broadway, although not typically with a chorus.
Doo-wop is another style originating in the African-American community, but with some similarities to classical music, and that features strong leads and complex backing sections.
If you're willing to go completely outside the classical tradition, you have quite a bit more to work from. African and African-diaspora music is almost always polyrhythmic.
- Shape of You - Ndlovu Youth Choir w/ Wouter Kellerman (Ed Sheeran)
These songs have solo lines that overlap the chorus:
Finally, here are some less classifiable, pop-influenced songs that do interesting work with lead and harmony.
As to how the lead is distinguished from the chorus, there seem to be several strategies used in different music and traditions.
- The lead is the highest voice.
- The lead is in overlapping alternation with the choir, a call-and-response pattern.
- The lead is a rhythmic contrast to the choir (short notes against long ones, or vice versa).
- The lead is essentially singing an independent song from the chorus.
- The lead is singing lyrics, the chorus sings non-lexical vocables.
- The lead has one rhythm, the chorus shares a different one.
- The lead line is first sung independently, and then repeated with chorus.