I am not surprised she won't life the lid. To her it is just a silver disk. The food is hidden and in her mind it is not there. As for the desserts, I am not sure if other's have had this experience but Mom and Dad both developed a major sweet tooth when dementia set in. Dad is hooked on pepperment candy and ice cream and Mom is a chocoholic. If given a choice between a sandwich and a piece of pie, both will grab the piece of pie first. When Mom was at home she used to say that you shouldn't save the best for when you were full. She would eat her Key Lime pie (her favorite) before her meal. Then have another piece after she ate.
In the AL they do use covers but they are clear plastic so you can see through them. Not only that they remove the lids for the resident when they set down the meal. They don't bring out dessert until AFTER the meal is eaten. This seems to eliminate the problem you are talking about.
From what you say I do believe that your mom needs meal assistance. This is something the hospital should provide and something you need to insist upon. They should be recording her meal intake, especially with her sodium potassium imbalance. There is no way they should take a full tray back to the kitchen without at least attempting to get her to eat something... whether you or your sister are there are not. It is their responsibility, not yours, to feed your mom while she is there. It may be that your Mom has just lost the desire/ability to eat but that doesn't mean she should not be offered food in a way that she could eat it if she would... even if that mean trying to feed her.
Keep us up to date on her progress and know we are holding on to the other end of the towels
Love, deb