Not quite correct. It is the outer faster turning wheel that unlocks when making a turn.
I once had a series Landy with detroit no spin Salisburies front and rear, and the front would occasionally drive only one wheel at inconvenient times, but it was a very high mileage well worn unit. The OPs Locker is presumably a new one, and if it definately only powers one wheel and there isn't a broken halfshaft or stripped drive flange(not uncommon on Defenders) there is something wrong with it, or it was incorrectly fitted. From memory there is a ''master'' tooth on each side of the central driver that must be correctly aligned with its mating annular ring for the unit to work correctly.A bent axle housing or loose wheel bearings could also cause the Detroit side gear to bind on its splines so that it doesn't always slide back properly into engagement after making a turn.
Failure to lock the centre diff for low traction conditions can sometimes cause the spider gears to friction weld themselves to the cross shafts, giving a limited slip or locked diff effect, until something breaks, so it's not advisable to see how far you can go at offroad obstacles with the CDL disengaged. while we are at it ARB airlockers are also prone to friction welding if disengaged in conditions that will induce individual wheel spin.
Wagoo.
Edit. I'm betting on a stripped rear axle driveflange.Reason, centre diff unlocked, vehicle struggles or stops on low traction climb,Mate behind observing power going to only one rear wheel, but may not be able to see that the front wheels aren't spinning either. Centre diff locked,vehicle proceeds because power now goes to front wheels and the one rear wheel with intact halfshaft/driveflange.

