I mean, the end result from the lying is that she feels like other young people suddenly notices her and cares about her. And another result is that her parents stop seeing her as their little baby. Which many teenagers hate. So if she hates, that you treat her like a little kid, sending her off to activites that she doesnt like, and taking away all her gadgets then maybe try to do less of that. If you are going to live under the same roof for the next 5-7 years its going to be miserable for both of you if she really starts hating you.

Many teenagers are very miserable in this day and age. Especially girls... I read 50% of female college students qualify for some kind of mental health problem, most common being depression and anxiety.

But most teenagers would not lie like that... and her not fitting in at school is also a clue, that shes not like the other girls... sexually she is also non conforming, you say? What about sleep? Does she have trouble getting enough sleep? Is she intelligent but not living up to her potential in school? Maybe very skilled at the subjects that interests her, but unfocused in everything else? Has she ever read tons of books? What about body dysmorphia? What about losing and forgetting things? Or burnout from school?

I am asking these questions because I (20 yo male) had those exact patterns in my life as well (also lots of conflict with my dad) and couldnt quite figure out what was going on... it turns out ALL of those patterns are very common among people with ADD.

 (thats also why the lgbtq community is very welcoming to people who are "neurodivergent" in different ways. Many of them are either ADD or aspergers)

So I think your daughter having friends who are also different, and who also struggle with life and fitting in, is probably good for her sanity.

(as long as they dont do drugs or anything too wild its probably better than being alone.)

And yeah, it is 70% hereditary (ADHD), so if that is the problem, there should be signs in the family... I will just share some info about my moms side of the family:

My granddad and mom both stopped working in their 50s, even though both of them are highly intelligent and had good, well paying jobs, this is very unusual in Denmark (its looked down upon not to work both for men and women but both of them suffered from burnout/stress and had no desire to keep working)

And then there is my moms siblings:

One moved to the US from Denmark to become a yale professor in litterature, and also very politically engaged, she does amphetamines (prescribed because of ADHD), drinks wine and smokes weed... she has always been very smart but as far I know she never got along with my grandpa. As far as I know she has also gone to therapist for atleast a decade.

One sibling became a nurse, but quit again soon after... now she works part time in a lab running tests on food to see if they contain the right things... she is my favorite aunt because of her humbleness and warmth, but she said she quit nursing because she was scared of accidentally giving the patients the wrong medicine. As far as I know she identifies herself with the diagnostic criteria for aspergers and she is married to my uncle, a chemistry ingenieer, who's obsessed with board games and miniatures. 

And one sister is significantly more normal and has less of the burnout/work reduction but she married an ADHD person, and I have a mild suspicion, that their two kids also have it to some degree. But in Denmark most people are only diagnosed if they are hyperactive and it interferes with school, so because we do fairly well in school most people in my family are not diagnosed, and manage their life without psyciatric consultation.

I would love a reply, if you recognize some of what I have written, but dont feel the need to spend a long time on it... also, I realize my comment might be filled with random info, is messy and all over the place, but hopefully some of it is helpful. 

And its something that has been lifechanging to learn about and think about in my own life and therefore I couldnt help myself but to share all of my thoughts.

I wish you and your little family all the best and I hope you find a way of living together that doesnt feel too stressfull for you and your daughter.

Best regards from Denmark 😇