gbuis:
I’d like to buy an LCD with at least 10 lines, and if possible one that runs on batteries.
There are plenty of graphics LCDs that would display ten lines of text, and they can all run on battery. All you need is a battery that is the right size.
I’d like to be able to move it around on my desk and wires kind of make that undoable. Is this possible?
You appear to have answered your own question. The main problem is probably the packaging, where a lot of effort will go into packaging a bad idea.
What do you recommend?
I recommend you sit back consider the situation, it can't be hard to think of something more useful than this. You could make a list using pencil and paper.