The trick here is to use a ceramic filter that have holes that are so small that only Lithium can pass through.

Actually the only "molecules" smaller than Lithium are Hydrogen and Helium. Helium is not a problem because it's too easy to pull apart and Hydrogen (H+ and H2) are not problem because H2 is another of the products.

(Actually^2 H+ is not isolated, it's combined with water in H3O+, but I guess the holes need some room for the water around the Li+ ions. The technical details are probably more complicated, but "small holes only allow H, He and Li to pass" is a good approximation.)

But Uranium atoms are huge. They are bigger than most atoms, and I'm not sure if the common form in seawater is a combination of Uranium and Oxygen. A hole that big will allow most mineral to pass, so you will just get brine. Using it in the other direction with holes just smaller than Uranium is also not very useful, because you will get Uranium mixed with a lot of crap, many of the contamination are not isolated atoms (that are mostly smaller) but molecules that combine a few atoms are are bigger.