I don't have a daughter, and if I did, she'd be getting on in years by now, but I have a niece I helped raise and am still in touch with, still love and vice versa. I was never trying to be her parent in my behavior. Two wacky parents are enough, she needed a wacky aunt. She was in foster homes at one point. I listened to her, I tried to give perspective, I tried not to undermine the parents and that wasn't easy as they were wildly different and at war for good reasons. I never lied from when she was two to twenty two. Sometimes I didn't explain things fully, especially in the early years. At this point we are more peers of very different ages. A day together is joy for both of us.
If I lived nearby, that pleasure would naturally fade to the grays of ordinary getting along, but we would still retain the old talk stuff out behavior - only this time not with me being the one full of knowledge, but the both of us with our accumulated experiences. She's always been psychologically attuned, watchful, and has grown into an adult I'm glad to know, and we have those conversations by phone, admittedly not often enough. She doesn't email, I don't text, and the phone is problematic. But when we talk, it's still straight.
On lies I was told - the usual here in the US, tooth fairy, santa claus, easter bunny. I think I didn't believe in the tooth fairy but went with it, sort of a game. I did believe in santa claus, had to be told by a friend it was a made up thing. I don't think the easter bunny registered much, as I had just turned nine when we moved to a suburban Chicago neighborhood that made a big deal out of easter. As in, large shrubs covered with colored egg shells type big deal. An egg dyeing afternoon.. I enjoyed all that, but I'm sure I never believed in some bunny.
Generally, though, my parents didn't lie to me. They kept silent charge of secrets I had no clue of which got to be an ominous undertone in my teens and worse later, but I can't say that I think they ever lied.
Religion - like some others, both of my parents believed and I grew up believing. I know looking back that they had very different levels of belief. Now, I'd bet my father was at least verging on agnostic; my mother was unquestioning and fervent. In both cases, whatever they said to me, I don't remember it as lies. My father was more quiet about it.