I am so sorry that this is happening. Some cats are really tough when it comes to accepting another feline into the house.

If Pippa is going to stay I would start by going through the reintroducion phase. Start by confining Pippa to one room (just like you would a new cat) so Lulu has the rest of the house to herself. The go about regaining Lulu's trust. She seems like the type of cat that does not have a lot of bravery. Coming to sleep with you only AFTER you are asleep shows that she is insecure. She wants to be close but still has some fear (this is probably based somewhere in her past).

After at least 1 week, 2 weeks if you can stand the seperation, reintroduce the kitten to Lulu with small interactions. Do not allow them to be alone together for a while.

Lulu may never like the kitten, but she should be able to learn to co-exist.

And by the way, if Pippa is still young things might improve immensely after she drows to adult size. Some adult cats do not know how to deal with small kittens.

Best of luck!