Just FYI, those .38 LC cartridges are probably from the 60s or 70s (I could be wrong), in any event, they are a bit less powerful than service-load .38 Special, clean, non-corrosive primed, and perfectly safe to fire in your M&P. As above, before you do, you might want to check around and see if there's any trade interest for a box of .38 Special 158 grain RNL (Round Nose Lead). That's the standard service load - avoid +P.
We will all love to hear a range report.

Larry