There are several aspects to a potential LMC.
Weight can go up or down or the CG can move either way depending on what's done.
Absolutely .. however LMC, while usually couched in terms of weight deltas, has little to do with weight as such and everything to do with IU (as an indirect measure of CG).
If the weight goes up with 4 extra pax and bags on a hot in day in Malaga pointing at the mountains for take off then it has everything to do with weight and how much poke is coming out of my engines - especially if one fails.