You could try... and you could blow up your gun, or worst.

.45LC has a larger, raised rim on it, .45ACP is the same size as the rest of the casing. The bullet would not remain in position and would cause you some problems. Use what the manufacturer recommends please.

Please allow me to make the point clearer:
Although a .45 ACP cartridge would fit into your Judge's cylinder, because its rim is the same diameter as the rest of the case there would be nothing to hold the cartridge against the pistol's firing pin.
Therefore, it is quite likely that the .45 ACP cartridge would just slide forward, deep into the Judge's long cylinder. It might even be driven forward by the firing pin's blow.
Since the .45 ACP case has no projecting rim, the ejector star of the Judge could not remove it from the cylinder, either fired or unfired. You may therefore end up with what looks like an empty cylinder, but instead you would have one or more .45 ACP cartridges stuck far down inside it.
If you then reloaded with .45 ACP cartridges, the stuck case (or cases) already in the cylinder would hold the second cartridge (or cartridges) against the firing pin. (A .45 "Long" Colt cartridge might also be able to slide in.) The hammer would fall and ignite the second cartridge's primer, making it go off into the rear end of the preceding, already-stuck case.
That would cause the cylinder to come apart violently, sending shrapnel into your hand, and probably into your face too.
As Zhurdan has already written, "Use what the manufacturer recommends please."