Rarely is there going to be a match in felt recoil between defense loads and FMJ target loads... especially between brands... And more so if you run +P ammo. (which there is pretty much no point doing, with modern loads doing as well or better in standard pressure)
If I recall correctly, the Lawman is supposed to be similar to the gold dot standard pressure of the same weight.
For now with price being equal, get 124gr... Later, if you are at a big box store, get whats on the shelf. I have not had any issues switching between 115gr and my 124gr defense loads. The difference exists, but it is not enough to cause problems.
I am not a top level shooter, honing myself to one load and one pistol for countless rounds, just to shave off a few hundredths of a second off my course times.
I shoot too many different pistols regularly, and they all feel different. Platform does more to felt recoil than the round used.