There really IS only one way to deal with this behaviour - that is for your DD to walk away from him.
Arrange contact for the child via a third party.
Have absolutely nothing to do with him that is not directly and specifically to do with the child and sent through that third party (which almost certainly should not be his Mum...).
In your shoes, I'd minimise concern for him - 'yes of course we hope he's ok'... don't speculate, don't let her worries get you wound up, be the calming influence.
Big up the message, this is NOT her fault, his mental health is not her responsibility, his actions are not HER responsibility, his choices are not her responsibility. The people responsible for him are - him, then his Mum, and mental health professionals. Not her.
DO NOT... tell her that he won't actually kill himself, or that he is lying - he might not intend to kill himself but do it anyway, he may be lying, he may not - but if he DOES kill himself and you've promised her it wasn't true, he wouldn't etc etc... thats worse for her. I have direct experience of this, people think it helps if they tell the victim of the abuse 'oh he won't ACTUALLY do it'... and when they do... its so so much worse for that victim. Just keep repeating 'whatever he chooses to do is his choice and his responsibility'.
Do your damndest to keep her away from him.