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To try and answer your question "Why does Lee like Angel?" I think, at least to me, Lee didn't really have a lot to live for. He stated how he longed to die, and didn't really have much of a purpose in life. Becoming someone who could help people may have staved off that desire to die temporarily, and when Angel opened up about their experiences, it sort of gave Lee a new purpose beyond helping a patient medically: getting rid of all of Angel's problems. Some of these include their co-worker, loneliness at home, and the costs of rent and transportation, all of these Lee helped Angel with, even if in his own twisted way. 

His obsession for Angel is very subtle, like when Angel would leave the room and the screen would be left on Lee just .. staring, before it goes back to Angel. As well as that one scene where he peers at Angel before quickly shutting it before they had a chance to spot him! Although not directly explained in game, once you notice them you can kinda correlate them right back to Lee's infatuation for Angel!