I would immediately put that little girl in her place! My suggestions would be to start paying attention to Ringo first no matter what you do~come home Ringo gets hello first, give treat Ringo first, on the bed Ringo first. Pebbles would do the same with Bogey and I was able to stop (get control) this by not allowing her to push ahead of the others.
There is dominance it height and when Lucy is on the bed she is higher than Ringo so is more dominant. My suggestion would be to not allow her on the bed if Ringo is not in the room and never allow her up first either. At least these are the things that work for me with Pebbles. Funny thing is the there is never an issue at my house between Pebbles and Doodlebug. Dbug just does not take her cr@p! If she growl at his or give him a look he totally ignores her and goes about his business or he will bark (loudly) and start hopping around to play. He's the punky little brother that just does not care what she says or does. Bogey on the other hand would hang back and be submissive to her so she will try to pull things like you are seeing with Lucy.
As for the food sounds like you need to stop feeding in her crate. Pebbles is also a food guarder and I could never put a bowl of food in her crate and expect to get it back without being bit.
When it is time to eat Pebbles now knows she needs to sit, give paw, shake. After she does this I put her bowl on the ground and I make her wait......wait.....wait
Then she gives paw again, shakes and she is allowed to eat. If she tries to push past me to the bowl I immediately stop her and will even pick the bowl up. Since I started this with her it's amazing how she now knows what to do. She is always fed first.
Is Lucy also pushing her way out the door first? Pebbles was doing that as well and I put a stop to this too. Now they are made to sit at the back door. I make them all wait until I say the can go outside. I started with treats and made them all sit and wait but now they will do it automatically. Pebbles will want to bolt out sometimes so badly she will twitch.
But I make her sit until I give the OK to got out.
I wish that there was a magic solution to guarding/dominance issues since I would be the #1 student. It's so hard when they are guarders. I think you can get it under control but not totally break this habit (at least I haven't been able t do it) and it will always be a struggle.