Friends child is a liar- Aibu to stand my ground?

[MyHeartIsInHavana]

I have a good friend who has children the same age as mine, all at same schools.
Eldest daughters also so many of the same clubs at school as one another- this means we share pick ups ie one of us collects kids from school and the other collects eldest children after club if one of us is stuck. Mostly evenly spread and abs this is appreciated by the both of us.

The issue is my friends eldest- she is increasingly telling lies, and lately these had included lies about me.
It started with lying that I hadn't brought her a snack and drink after school (strawberries and cartons of apple juice) and had only brought enough for my daughter. Complained to her mum that she was 'starving' and upset because my daughter had a snack and hadn't offered her anything. In truth I took two matching Tupperware tubs of strawberries and her daughter ate them all while my daughter only had a couple. If she was that hungry she could have eaten the rest of my daughters that I offered her.
I explained this but my friend just laughed it off saying maybe her daughter forgot.
Then it escalated to a party invite. Daughter was invited to my daughters party. We sent invites out in book bags at school and I text the parents- including my friend. Her daughter then said to my friend that I had asked for the invite back apparently because too many children had accepted and there wasn't enough space- not true, it was a disco in a hall. My friend confronted me about it and I said it wasn't true as a) it didn't make sense and b) I had text her as well as sending out paper invitations.
Today it's happened again- another lie- and my friend instantly believes I have done something unkind.

At the same time friend has been called into school several times as her daughter has stolen a class mates show and tell and previously lied about a teacher (small lie, nothing huge, but still called out on her dishonesty).

How can she not see the pattern?!
I don't want my daughter around his behaviour, and I'm worried how far this behaviour is going to go!

We have known each other years.
Aibu to confront friend with her daughters lies and risk losing our friendship?

I have a liar for a child, it's got worse over the last few year's, no amount of talking, punishments, time outs, have worked. The lies seem to come out of their mouth so easily. I have tried everything, gp, counsellors, boundaries in place, calming down techniques, this is mainly for the daily, angry outbursts. it's exhausting, I hate the fact that they are so unhappy that they have to lie.

I would reiterate what others have said and just don’t leave yourself vulnerable - I’d probably just say to your friend you’d like to remain friends but the lies are getting out of hand

I can't believe how common this is. It happened to me last year - my friend's DD told her I'd shoved her and was instantly believed. It destroyed our friendship utterly.

I was going to advise something other than cutting contact but I suspect that in Y6, this is probably your only option if you can do it sensitively - will they be going to the same secondary? DD had a similar but different situation in Y2 where another child was telling her deliberately hurtful lies, and I found that calling the child out and making it clear that I would be talking to her mother/teacher/other responsible adult stopped the behaviour in its tracks. It took a couple of goes but I did as I said and talked to the other adult both times and it became clear to the child that I wasn't going to take anything she said to me at face value so there was no point in trying it on. Also, the other adults were rational and sensible and could see what was going on, which helped. I also advised my own child to make it clear that she didn't believe whatever the child was saying and to tell her clearly that she didn't want to hear it and was going to tell me what had been said. It did work but I am not sure it would be as effective with a child of this age.

The other child in our scenario is still a bit of a troublemaker at times and enjoys causing drama between others but thankfully my own child has been left out of it. It was a really odd time and really strange behaviour from the child who comes from an apparently happy, calm and well-ordered household - so I really don't think it was a case of the behaviour being a response to stress in her own environment. I'd have handled it differently if I had thought that the child might have serious problems. Might that be the case for this child? In that case I would talk to the school on the level of 'I am worried about Amy (or whoever)'.

I'd be stepping back from helping out and making it clear why if asked.

Many years ago when I was at senior school there was a girl on the periphery of my group of friends,who used to tell silly lies. We all used to believe her stories until she was proved to be untruthful in small ways. I remember once she told us in great detail how her dad was a marvellous cake maker and had made her birthday cake. At her birthday party we all gathered around and praised him, he was astounded, as an oil stained mechanic he had never made a cake in his life he told us.
Her lies started in this small way but then in a French class one day she was in trouble with the teacher for some little transgression and she accused him of sexual impropriety. We all knew she was doing it to get back at him. This was in the 1980s and it was all dealt with in a low key way, it would be treated far more seriously now.
I often wonder what led her to tell so many lies. I bumped into her again after twenty years and she pretended that she didn't know me.

There was a girl like this at my school. She said that her entire family had died in a car accident and everyone was very sympathetic. The truth was that her stepfather was beating her up and she was in a foster home. Poor kid.

I know someone who told some strange lies, worst one was when she claimed she was in a sexual relationship with her twin brother. She didnt have a twin. Later we found out her father was on a sex offenders registered.

I'd send a text saying that you can no longer share lifts due to her dd's behaviour. Tell her this is the third (?) time she has made up outright nonsense about you and you find it hurtful, unsettling and offensive.