I have 100 rounds of once fired Lake City brass that I plan to load. I've heard that this brass has less volume than the Winchester and Remington brass I currently use. Will I be able to load it to the same specs. as I currently load or will I need to start from scratch?

Normally military brass is thicker and holds less volume. You should load at least 10% below your load in commercial brass.
Also, the military brass is going to have a crimp on the primer pocket. This is going to have to be removed prior to your installing a new primer. You can get a hand reamer to do this or RCBS makes a primer pocket swager die.

Whether or not you need to reduce the load for military brass depends on how hot your loads for commercial cases are. If you are near max., then drop back 10% and work from there.