The throttle delay on an un-updated LR3 / RRS is VERY VERY sluggish.

FWIW this transmission (ZF 6HP blah blah) was somewhat unique at the time in that I believe it was able to un-couple almost entirely from the engine to reduce load and fuel consumption. The down side is that incorrect programming would create huge lags I'd imagine.

Anyways a software update totally fixed the problem on my RRS, but I'm less optimistic about the LR3 since there were numerous complaints in the vehicles service history records and I think twice the dealer noted that they updated the TCM software.

There is a LR TSB for the issue, which also notes a delayed shift in traffic (plus the THUNK when it does shift) and some other things.

I believe the TSB instructions state that the engine management software must be updated at the same time (understandable since they communicate throttle and loads during shifts, etc) - perhaps the dealer forgot that part which would be embarrassing but I've seen crazier things happen before.

There were like 6 module updates from the body control module (the way the park distance turns on and off, the bluetooth pairing functionality, etc) to the electronic transfer case module, ECM, TCM blah blah.

I would definitely do that first.

Also it's a spec fill on these, so you won't be able to check / top off unfortunately.