Downshift Jerk from 2nd to 1st
 

I would start with software updates. Its unusual for a car to go 14 years and not have them done, but I certainly would not hang any parts on the vehicle until I knew the software was current.
There is a TSB for this very issue

TRANSMISSION DOWNSHIFT FROM 2ND TO 1ST GEAR IS HARSH

Situation:

A customer may report a concern that the gearshift is harsh and results in a thump or bump when the transmission shifts from 2nd to 1st gear. This condition occurs when the throttle is applied following a deceleration where the vehicle is slowing to a near stop. This condition can be intermittent and can vary depending upon the amount of throttle that is applied.

Action:

Should a customer express this concern, verify the condition and refer to the Repair Procedure below to update the Transmission Control Module (TCM). Check and, if necessary, update the Engine Control Module (ECM) software also.

Yes, good advice. I was fearing that, actually LOL - scared of the dealer...

I found the ZF trouble-shooting manual, and it says 1. check fluid level, 2. check binding of cable, 3. update software...

How would I go about the cable binding? I didn't really understand why an outside cable and lever would affect an internal downshift, and I didn't have any procedures to follow, other than remove the bolts and spray some grease around the moving parts, and then put it back together feeling like I'd wasted time... so maybe I could try that again properly before going in for the software update?

How does one do a software update is an older LR (2007 LR3 V8 SE)? As far as I know it has no wifi hotspot, has no touchscreens, no SIM card...Is the software updatable? Is this something that a GAP tool could be used for?

Dealer visit required

I have heard that the GAP Tool can do updates, but since I only use the factory tool, I cannot verify.
You don't always have to go to the dealer, there are independent shops like myself that have factory tooling. We do software updates on a regular basis.
Try LRSHOPS.COM

Is it possible to check what version software is installed to see if its been updated previously ? I have the occasional thump but my main issue currently is a failure to downshift from 3rd to 2nd or first and then when load is applied a transmission fault special programs off message on the dash - no fault codes logged though ?

You need a tool like Factory, Autologic, or Gap to figure out if its up to date.

Thanks. Can you use those tools to download a software update or just to determine if the software is updated...obviously you have to connect to the internet somewhere ...do those tools have that capability?

The GAP tool would allow you to check the software and update. They have excellent customer service and its the cheapest of the listed tools.

Lucky8 has the best prices on it.

Good luck!