The literal meaning of "morning sun" is just the sunlight that shines in the morning. The ambiguity creeps in with the line "my morning sun is the drug..." which could either mean that sunlight has replaced drugs in his life, or conversely, that drugs have replaced the sunlight.
The band members seem to have given conflicting statements on whether the song is actually about drugs, but the word from the songwriter is "yes", an interpretation supported by the fact that original lyrics apparently featured the statement "When I was a very small boy, very small boys talked to me, now that we've grown up together, they're all taking drugs with me."
Given all that, I would suggest that the narrator of the song is far gone enough as a drug abuser that drugs have replaced his former morning pleasure in the sunlight. He used to take delight in the morning sunlight, now he's glad when it's shady, because his new sunlight is the drug. Even so, there's still some ambiguity in the line "my life would depend on the morning sun." Is it that he feels his life depends on the drug? Or is this referencing that it's no longer a given that he'll be alive in the morning to see the actual sun?