[catlover2]

If feeding the cat first doesn't work, keep the cat in a separate room over night, feed cat first its breakfast in the room since she considers herself "alpha", then let Lucy outside to pee/poo and feed Lucy after she comes back in. When Lucy's finished eating, let the cat out of the room.

If the cat is aggressive to Lucy at other times thro the day, your mom should let cat know that she will not tolerate this. Your Mom is going to have to be the "alpha". She should have a spray bottle with water handy and spray cat immediately when it shows any bullying or aggression, and at the same time say a loud PSSST! and "No!" to the cat. Then redirect the cat with a toy. She should balance this out with praise and reward good behaviour. When the cat is behaving well close to the dog, praise and pet the cat and give it a treat (she'll have to give Lucy a treat too, but after the cat). Let us know how things work out.