The locking hubs only connect the front hubs to the differential. Obviously they are locked or the front tire wouldn't be throwing mud. Doesn't say anything about locking or limited slip (aka positraction) differentials.
Here's a site I found that claims to have the equipment codes for Ford differentials. That would at least tell you what the truck had from the factory.
https://www.drivetrain.com/parts_ca...d_ratio_do_i_have_in_my_ford__is_it_posi.html
You can also check for limited slip by jacking up both wheels on an axle and turning one wheel (transmission or transfer case in neutral). With an open (non limited slip) diff, the other wheel will turn in the opposite direction. With limited slip, it should turn in the same direction as the wheel you are turning.
Another test is to back up around a corner. With LSD, it frequently won't turn smoothly, you get kind of a waddling motion as the diff grabs and slips.
A little background: When turning a corner, all 4 wheels follow different paths and move slightly different distances. The differential(s) is what allows for this relative movement, by letting the wheels on an axle turn relative to each other. An 'open' diff applies equal torque to each wheel, meaning that if one wheel does not have traction, it will spin uselessly and the other wheel will only get as much torque as the spinning wheel (ie not much). There are various designs of limited slip, but the most common design uses metal clutches to transfer some of the torque from the faster moving wheel to the slow one. Unfortunately they are somewhat expensive, require special oil, and the clutches wear out in time.