Lionel Croy is without doubt the worst human in this book. Scratch that: he's the worst thing in the book. We like him less than we like Milly's tuberculosis. We hate him so much we are really tempted to punch the pages of the first chapter of The Wings of The Dove every time we read it.
Lionel Croy is just a walking ball of selfishness, and he has left permanent emotional scars on his daughters Kate and Marian. As Aunt Maud bluntly puts it to Merton, "They've the misfortune to have, I suppose you know, a dreadful, horrible father" (220.127.116.11). And it's not like this judgment is coming from nowhere. We can see pretty clearly for ourselves that Lionel Croy is a bad dude in the opening scene of this book.
For starters, he deserted Kate's mother after treating her like garbage for years. And even though Kate has still decided to stand by him, he rejects her love and tells her to do the practical thing, which is to never visit him again and to collect Aunt Maud's money—and, oh yeah, send it to him secretly. In other words, he chooses the possibility of money over his own daughter.
When asked at the end of the book whether Lionel is sick, Kate can only answer, "Father's never ill. He's a marvel. He's only—endless" (18.104.22.168). In other words, the man can't be ill because he's too evil to be ill. When the world ends there will be cockroaches, Twinkies, and Lionel Croy.
He's a scoundrel and a liar and there's no point in trying to pin him down on any issue. The only thing Kate knows for sure about him is that "[He is terrified] of somebody—of something. He wants, he says, to be quiet. But his quietness is awful" (22.214.171.124). His terror might come from the fact that Lionel knows he's lived a terrible life and has hurt many people.
James seems to stick him into this book mostly to help excuse Kate for being so cynical and opportunistic. Every time we want to judge Kate harshly, James seems to throw Lionel back into the picture and say, "But check out how bad her father is. Have some sympathy!"