I have just made some home-made Carpaccio from thinly sliced beef rump, lemon juice, olive oil and Parmigiano.
Is it safe to keep the Carpaccio in the fridge for 24 hours?
It was safe to keep the rump, so why wouldn't it be safe to keep the slices of the rump?
The only way that, according to USDA suggestion, it wouldn't be safe is if, in your preparation, you'd left the raw meat out of refrigeration for longer than two hours. These guidelines are generally conservative, but bacteria can grow quite quickly in meat above 40˚ F (4.5˚ C), and even more quickly above 70˚ (21˚C). Meat that will be served raw should be kept as cold as possible -- chilling your equipment before preparation is often a good idea.
The issue, to my mind, is that it sounds like you've already applied lemon juice. Being acidic, that juice will denature the proteins in the meat, changing its texture -- making it "mushy". (This is why marinades often contain acid; up to a point, this action is perceived as tenderizing.)
There's also likely to be some unpleasant-looking and -tasting, oxidation -- and/or maybe dehydration -- of the thin pieces of meat while they sit in the fridge. This isn't unsafe, but it does decrease the appeal of the beautiful rosy-red raw beef you're supposed to have. Rubbing on some oil may help with this problem, as might plastic wrap directly on the surface.
I'd recommend preparing the meat as close to service as possible and dressing it, at least with the lemon and cheese, at the absolute last moment.