Ahhhh-hah... I figured out the problem.
If I manually run the command:
"C:\Program Files\VMware\vCenter Server\python\python.exe" "C:\Program Files\VMware\vCenter Server\VMware Identity Services\lstool\scripts\lstool.py" list --url https://vcenter.domain.local/lookupservice/sdk"
Then I get good output.. Command works awesome.
But just as a hunch I had to check something out, I decided to see what happens when I run the same command with the '--no-check-cert' switch like as follows:
"C:\Program Files\VMware\vCenter Server\python\python.exe" "C:\Program Files\VMware\vCenter Server\VMware Identity Services\lstool\scripts\lstool.py" list --no-check-cert --url https://vcenter.domain.local/lookupservice/sdk"
...and guess what? I got the SAME java error as in all the other scripts: "peer not authenticated "
So then I went over to the VMware lstool scripts folder ( C:\Program Files\VMware\vCenter Server\VMware Identity Services\lstool\scripts\ ): and opened lstool.py with notepad and could see that it simply invokes another script in the same folder called: lstoolutil.py
I then opened that script lstoolutil.py in notepad and did a search for the string: --no-check-cert ...and there were 5 instances where various commands were calling this switch. So I commented out ( # ) all 5 lines calling this switch, saved file, and re-ran the original script: ls_update_certs.py ...and WHAH-LAHH Hooray!
Line 52: # "--no-check-cert",
Line 74: # "--no-check-cert",
Line 85: # "--no-check-cert",
Line 121: # "--no-check-cert",
Line 139: # "--no-check-cert",
Then just to check I run again: "C:\Program Files\VMware\vCenter Server\python\python.exe" "C:\Program Files\VMware\vCenter Server\VMware Identity Services\lstool\scripts\lstool.py" list --url https://vcenter.domain.local/lookupservice/sdk"
...and can confirm that all of the service registrations show the 'SSL Trust' field using the new certificate key.
Problem solved.. Let this simply a a journal for others to follow in case they encounter the same issue...