Here's a good FAQ on lockers:
FAQ for Differentials
Lockers make a big difference, especially in snow/mud. I'd put one in the rear before the front, i think you'll have better overall handling. Where you live matters, up north, a tire change helps get through the winter where LTX A/S tires are useless in snow.
Some lockers, like the Detroit Softlocker forces both wheels on an axle to turn (100% positive lockup) while allowing the outside wheel to turn faster in a turn. Automatic, no switches necessary.
You need to be careful with an eLocker on the front. Locking it effectively creates a "solid axle" forcing both wheels to turn at the same speed. So
you can only lock it on straight lines or snow (whether front or rear). You loose steering while they are locked. You only engage them when stuck or fear of getting stuck. That said, the day to day ride IMHO is better. Because both wheels turn at the same speed, manufacturers often install them with "smart" electronics that disable them at speeds above around 20mph.
I've had a bunch of lockers in my offroad trucks including Detroits and Auburn electric lockers. In my Ram, I change out the tires for winter to an M/T and that's good enough for me. If I were to install a locker, it would be in the rear (first) and an eLocker. Detroit softlockers are nice, especially not in snow on the freeway.
I spent the weekend running trails (snow over sand) and used my Auburn eLockers (other truck, not Ram) all the time. Would have gotten stuck numerous times without lockers. You are absolutely correct, LSD isn't 4WD - it's a lot closer to 2WD than most people think.