The 27-year-old has penned an open letter to the former Genesis star in her new book, saying she had learnt to accept the "sadness and anger" she felt towards him.
In an excerpt published by the Daily Mail, she wrote: "I forgive you for not always being there when I needed and for not being the dad I expected.
"I forgive the mistakes you made. And although it may seem like it's too late, it's not. There's still so much time to move forward.
"We all make choices and, although I don't excuse some of yours, at the end of the day we can't rewrite the past.
"I'm learning how to accept your actions and vocalise how they made me feel. I accept and honour the sadness and anger I felt toward the things you did or didn't do, did or didn't give me."
The letter is featured in Lily's debut book, Unfiltered: No Shame, No Regrets, Just Me, which is a collection of personal essays.
She also describes her battle with anorexia and bulimia, which she links to stress caused by her father's divorce from third wife Orianne Cevey, according to the Mail.
"Not only did I start viewing myself differently physically, but I began limiting my happiness by controlling my eating habits," she wrote.
"I couldn't handle the pain and confusion surrounding my dad's divorce, and I was having a hard time balancing being a teenager with pursuing two different grown-up careers."
Lily, who was born in Guildford, Surrey, but grew up in the US, reportedly describes the "terrible disconnect" that grew between her and her father as she got older.
"Many of my deepest insecurities stem from these issues with my dad," she wrote.
Lily, who is the daughter of Collins and his second wife Jill Tavelman, was nominated for a Golden Globe this year for her role in Warren Beatty's Rules Don't Apply.
Her father Phil has four more children from two other marriages.