I would love for that to take place, on both counts. Unfortunately it will take a sum of things to push her to her breaking point, but with the cumalative efforts on all parts she may very well snap.
Lucy and Paimon ought to hang out, a pseudo-father figure (being that Paimon is a father, is older than him and Lysander craves paternal attention, he will make this so) in the form of a should-be loyal "pet" will be interesting. And Beelzebub may be the person he shares most of his worries with. I can't quite place it, but there is something about Beelz that is welcoming. Flauros~, Malphas~. Lucy only wants to love you. Sometimes. And Amdusias, you be cray. Why avoid the party?