I'm so sorry about Lucy Cat.
It sounds like she has accepted and has ;left her alone, so take Lucy away. Lola may have known before that Lucy was gravely ill.
Just feed Lola as normal, with some extra treats of stuff you know she can eat, if you want to, as and when (I tend to use this as a way to check if they are eating). Spend a lot of time with her and see what happens.
She may be ok, she may need a friend straight away, she may want to be your friend.
Time will tell, but Lola is in the best place, with the best care and a fab owner. Hopefully she will be fine.