First off, I'm assuming you mean the .45 ACP and not the .45 Auto Rim, and second off, I do not reccomend that. Although it may be possible, the .45 ACP die is much shorter than the .45 LC, so it will only size part of the shell and if done repeatadly (or even just once), the fold caused by the two diameters could cause the shell to crack and could harm your gun and more importantly you. This problem could be even bigger if your chamber is out of spec and it causes the shell to expand more during firing. I am certainly no expert on this, but it's just not something I would risk when you could buy a new die in the correct caliber for under $40 (for a Hornady, atleast).
As for the vice versa, certainly not. I'm assuming since you said dies and not die that you mean both the seating and resizing die, in which case the .45 LC case is much longer and the die would crush the smaller .45 ACP case.
John