Electronic Diff Locks (EDL Traction Control) dont do anything until the mechanical diffs have done all they can do, if your wheel up in the air and the diffs try to send power to the free wheel it senses the wheel's speed and applies the abs pump to just that one wheel and allowing the diff on that axle to power the wheel thats still on the ground instead of stalling out..
Adding a LSD to low speed/offroad traction control just results in it taking more effort to trigger the TC systems, if you were to add a locker the'd never engage because the wheels would spin the same speed regardless of how much traction they had.. so generally TC plays well with all mechanical diffs.