That is an interesting one. First, as you said, you really, really want to avoid having any accidents as that will just confuse Lola and it really won't be her fault.
Perhaps you could put a comfy bed in your kitchen area (tile floor area) and secure her in there, either with baby gates, or an "X" pen, or doors if your house has them. I would start that by introducing it to her slowly on the weekends and building up to longer and longer times. Right now, as much as we feel they are cooped up in their crate, they find their crates to be their safe place. Think of it like their personal den.
Actually, put her crate in the area in which you wish to keep her confined, but leave the door open! It takes me a minute sometimes.
You will probably find that she likes to sleep in there even though she has free roam if she wishes. Again, build up to this new found freedom slowly.
I know she is 3 already, but do get down on your hands and knees and make sure there is nothing that she could possibly get into that may harm her, like the garbage, electrical outlets, etc. Give it a whirl and see what happens.
Do let us know how it goes!