Short, simple answer - no. Even if you could use the same sizing die for both cases, you couldn't use the same crimp die. It's not like loading for the .38 Special and .357 Magnum, which I see from some of your other posts, is what you're familiar with.
The 45ACP and the 45LC use different shell holders too.
The good news is both use the same size primers, and some of the same bullets and powders will work for both cartridges.