I had the same issue. Rpms would stay steady in manual mode. Definitely a worn out torque converter.
However, I fixed mine by replacing the tranny filter and oil.
Could maybe fix yours. My car had 120000 miles on it when I noticed the fluctuations.

Changed tranny fluid last week and the filter. No change at all unfortunately.

It actually took my car like a month for it to stop after I changed everything. Idk why it wasnt instant, but it took a while for it to settle down.

Also wanted to ask, how do I check if the transmission software updates have been done with my GAP Tool. I would move forward with that update before looking at torque converter.

Ask GAP, they'll help you figure it out.

Really? They used to be so helpful; now they don't even respond and if they do it's really short answers. Pretty disappointing considering I have the BT IIDTool with two VINs registered...and have pointed umpteen LR3 owners towards the GAP tool.

No way to find out but asking. That is unfortunate to hear though houm.
They were helpful with the last question I had for them a few months ago.

2006 4.4l HSE non-supercharged
 

I just purchased a 2006 Range Rover HSE and occasionally ( mostly first 2 miles) the rpm fluctuates in range of 1500 and 2200rpms. I’m suspecting the APP sensor as the only fault code on my OBD11 module is bad heater element. Engine light is illuminated and I also get sluggish acceleration from 0 for about 3 seconds when I first run the vehicle. Please help as this is my first rover and like everything about except potential torque converter issue

Read the files attached earlier in the thread. A faulty APP will log faults and put the vehicle into a limp mode.

Surging RPMs while driving is classic torque convertor issue. Lag when initially accelerating is probably also torque convertor related. Sometimes you can get lucky with a transmission fluid and filter change.

Hi all,
Sharing my experience. 2008 LR3 HSE (4.4 L) with 105k miles. The RPM surge started about 1000 miles ago for no reason (that I can tell). RPM's do not fluctuate if in cruise control or manual mode. Symptoms started getting worse when going uphill although threw no codes.

We own 3x LR3's (veteran non-profit) and I swapped the APP Pedal Sensor with no result. Took it to a highly regarded repair facility in Salt Lake City that specializes in Land Rovers and told them the symptoms and that I believed it was the torque converter. They said it was the rear differential and $3k later to put a used rear diff in there (apparently they don't make new ones) the problem still persist when we picked it up today!!! Took it back to the shop (which was closed) and did the key drop and going to deal with them on Monday.

*We got several thousand dollars of other work done too while it was there including a transmission service/ seal service, so don't think the problem is related to the transmission.

QUESTION: How would you all go about dealing with the shop? My first thought is to have them refund me the entire cost for the rear diff parts/ labor as it was completely unnecessary. If they do that I'm happy to pay for the parts/ labor for the torque converter.