Speaking on STV's In Conversation with Bernard Ponsonby, Ms Davidson, 41, said she was worried about her mental health while working as part of the Better Together campaign.
She said she would "never not have time" for the former Scottish Labour leader for the help she gave her.
Ms Davidson told the broadcaster: "During the referendum, when we were involved in Better Together, I can never thank Johann Lamont enough for how much she put an arm around me during that.
"I was young, I was new to this, it was something big, there was a lot of pressure involved, and she was honestly really helpful and caring, and I will never not have time for that woman.
"Our politics are massively different, and she always treated me slightly as if I were an errant niece in some kind of way."
In the candid and emotional interview, the former Lothians MSP also opened up about how parenthood led her to resign the leadership in 2019 and about always being open about her sexuality in politics.
She added: “One of the things being in broadcasting in Scotland for years had taught me was that even people who don’t follow politics hugely can tell if you mean what you say and they can tell if you’re not answering a question. I didn’t want to be ‘the gay politician’ or ‘the gay Tory’ – I had lots of things to say, I talk very fast, and I try to say lots of things all the time. I thought there was more to me than that.
“It wasn’t something I was willing to compromise on; I wasn’t going to lie. I wasn’t going to make it a dirty little secret – I don’t believe that it is and I’m not going to pretend that it was some sort of hindrance or something that was holding people back, because it shouldn’t be and it isn’t, and I guess it’s part of being honest.”
The interview is now available on the STV Player.