The ambiguity of whether Legion takes place in the actual X-Men Film Universe or its own parallel universe makes sense when one considers David's fragile mental state alongside his powers; it's possible that while Legion may be part of the X-Men world, David is living in his own reality.
Alternately, the fact that David is a Reality Warper of unimaginable power means the series can very well take place in both its own universe and the X-Men Cinematic Universe.note For that matter, should Fox and Marvel ever decide to combine their universes, Legion could very easily become the means to do so.
It's convenient that he's diagnosed as a paranoid schizophrenic because one of the most common delusions/hallucinations associated with that disorder is being chased by the government. Also, the overarching plot; he's apparently not sick at all, he's one of the world's most powerful mutants, and the government is chasing him / his friends have secrets. I.E: non-awareness of mental illness symptoms, paired with grandiose as well as paranoid delusions, lampshaded by David in season 1 finale.
Considering Legion's single greatest claim to infamy is traveling into the past and murdering his own father, triggering the Age of Apocalypse, it's also possible it's a tangent timeline to the main X-Men cinematic universe.
The Devil With Yellow Eyes is more than just a scary name. In many ways, he's a perfect representation of Old Scratch himself. First and foremost he's a tormentor of souls. He terrorizes David and anyone else he comes in contact with. Second he seems to be pure evil, visibly relishing terrifying of and even harming anyone he can simply because he can. Then, there's his power, having enough power in David's mind to enter and warp memories on a whim, nullify an experienced mutant's memory powers and even fool a powerful telepath with an illusion strong enough to cause her physical pain. Much like how Satan is the absolute ruler of Hell. Finally, there's the true meaning of the Devil's name. "Ha-Satan" could be translated into "Adversary", and TDWYE is David's ultimate Enemy Within.
The beautiful forest surrounding Summerland (According to David's narration "-The place they said didn't exist") echoes the forest-centric decor of Clockworks.
In Chapter One, during the dance sequence, Lenny is doing her own thing, away from the others, which is odd considering that David has everyone at Clockworks as part of the dance number. Then you realize that Lenny is the Shadow King; try as she might, she's not 100% a part of David's mind and can't fully fit in with the group.
In the first episode it was shown that David apparently tries to hang himself, although, as David's therapist mentioned, while he had rope burns on his neck, there was no cord or rope to be found. Now, knowing that the Shadow King was inside David's mind since he was a baby and was trying to take over his body, was David's "suicide" really the Shadow King's earlier attempt to try and take David out?