Land Rover Discovery 3 loss of power when towing caravan

The topic is a Land Rover Discovery not a Pajero - the LR already has a lock up torque converter that locks from 1200rpm.

Ozziecruiser,
The Pajero has OEM lock-up too, but only in 4th and 5th, and the lock-up often doesn't work in 5th when towing; this why most people get better economy in 4th when towing, rather than leaving it in drive.
I am not aware of how the TCU controls lock-up in the Land Rover gearbox, but it is common for OEM lock-up to only occur in the top couple of gears, whereas for towing uphill, and engine braking downhill, you really need lock-up in lower gears. The additional benefits are lower ATF temps and better economy.
My suggestion to consider a lock-up kit is independent of the type of vehicle, but I mentioned the Pajero as an example of the benefits of fitting such a kit.
Whilst I am aware that there are quite a few after-market lock-up kits for Toyotas, Nissans and Mitsubishis, I am not aware of one for the Discovery.
PS. I have owned three LR vehicles over the years - a RR, a Discovery, and finally a Freelander. Fantastic vehicles when they are running, but the last two were genuine off-road vehicles i.e usually off the road in a garage somewhere being fixed!!

Has the LR got a lockup torque converter that stays locked ? I’d say not…just like most auto boxes.
No matter what make of car (4wd), the auto will change down going up hills, and if towing a big load, the auto will not be locked.
A lockup kit will stop a lot of slippage as the auto will be “locked” in any given gear.
So to answer the OP’s question…..yes the auto COULD be overheating and going into a limp type mode. The OP should run a Ultragauge or similar and keep an eye on his trans temp.