I would love DD to leave but she's tied in to live here till July! So can't rent elsewhere as can't afford it.
OK, so assuming they are jointly named on the rental agreement?
Then, honestly, I would say it's time you daughter makes formal notice, posted signed for in writing, to flatmate of her intention to move out. Unless of course they could have a conversation about it, but that sounds unlikely?
Daughter needs to state that the current situation is no longer working for her and that she will be moving out unless L wants to move instead, and that she will be advertising the room to find someone to take over the remaining lease.
And then do just that.
And if flatmate doesn't respond, then go ahead and do it anyway.
Life doesn't stop for, or revolve around, the flatmate. If she won't get involved, it will happen to her, rather than with her input.
Advertise the room share, find someone to takeover the remaining lease and pay the deposit, so your daughter can get hers back, and move on.
When I was a student I had to do this and know many people who did.
It's a total wrench to move again when you think you've got that all sorted, but it's absolutely do-able for your DD to move out.
It is worth checking if the rental agreement has a 6 month break clause or some such thing, as then DD could force that they both move out and the property be re-let with minimal fuss.
There may be will be some admin fees to swap names etc. on the rental agreement if someone takes it over, but that's a small price for your daughters mental health and wellbeing.
I don't think there's any point in worrying over what might have happened, why L is behaving so badly, what could have caused it etc. etc. It's time to be practical and help your daughter to put her wellbeing first. It's an important lesson in self respect and standing up for your own needs and having faith in your own reality and experience of a situation, which although painful can be a very powerful lesson.