By now, I think it's fairly clear that Lenny is the yellow-eyed monster on Legion. Her destructive dance through his mind palace at least seemed to confirm that she is controlling this fantasy, and has been tampering his memories. However, an even more interesting revelation is that apparently, Lenny knows David's father on Legion — who, as you may remember, is Charles Xavier in Marvel comics.
What's confusing to me, among other things, is whether or not the Monster/Lenny is a parasite in David's brain or just one of his mutant personalities. She said that she had been with him since the womb. In the comics, David creates these personalities to house different mutant powers, but that's not what this sounds like. I know that, at this point, I should probably let the Legion comic book history go and roll with what the FX series is presenting instead, but it's so hard to make sense of what's going on with David Haller that you have to grasp onto something.
While it would be cool if Lenny was once a real person who knew Charles before David was born, I think what she means is that as a parasitic creature, she has memories of him from before David was adopted. In David's memory, his father's face is obscured — something that the Monster/Lenny could have done.
I do really like how Professor X is vaguely referred to on this show. Lenny kind of laughed at how everyone thinks David's father so great, yet he abandoned his only son. When you consider how easy it would be for Charles to check in on his kid, it's even worse! He can be anywhere and read any mind. So easy. Did Magneto make David's mom a feelings helmet too? It seems like more and more clues about the X-Men universe will drop as the series progresses, but never in a way that ties it too strongly to any existing property.