UPDATE:
On the 3rd try, the dealership did adjust the parking brake to my satisfaction - Enough "hold" without any vibration. As for the tire wear, I ended up buying a set of 4 new tires as the old ones were very worn already, especially the fronts (typical inside wear for the IS). At the same time, got an alignment with more toe-in up front (unrelated to the parking brake issue).
Thank you, Sasnuke, for your detailed reply.

Original Post:
2017 IS200T. The parking brake pedal had a lot of travel before catching. I have to press it to almost touching the floorboard to engage the brake. The dealer adjusted the brake under warranty, and it worked great! EXCEPT then the car started vibrating severely at random times. Returned to dealer and the service advisor acknowledged that the parking brake was not properly adjusted. They re-adjusted the parking brake and it's now back to the original state - ineffective, but the severe vibration went away.

• Was the mechanic simply unable to properly adjust the parking brake on both occasions? Or could something else wrong with the parking brake?
• The car has more road noise now and I fear that the awful vibration damaged the tires (or worse, suspension bits). Both rear tires appear to have some scalloping (uneven wear like teeth of a gear). Could the badly-adjusted parking brake have caused the uneven wear? What else could have been damaged?

I'm planning to return to the Lexus dealer (under warranty), but would like to be armed with knowledge of ClubLexus.

 

25,000 miles

Right rear jagged wear, inside

Left rear jagged wear, inside

 

The vibration would be an indication that the parking brake was too tight. Now it would appeared they have loosened it off too much, so you are back to square.
Other than the parking brake shoes and the rear rotors, it being too tight wouldn't have effected anything else.
From the pics you can see feathering across the entire tires, which has obviously been going on for some time.
I would suggest an alignment if you haven't had one recently.
The increased road noise is likely from the feathered tires.

To properly adjust it they really need to take both rear wheels off and adjust the parking brake as loose as possible.
Then go inside the car and release any tension on the parking brake pedal adjuster.
Then go back to both rear wheels and adjust the parking brake until the shoes are just touching the inside of the rotor...then go back to the pedal adjuster and remove any slack.
This way when you press the pedal, that will engage the parking brake tightly.
There's no point adjusting the pedal if it's not adjusted at the wheels properly, and vice versa.
It's not a 5 minute job...if done correctly...it should take 30-45 minutes once the mechanic hops into the vehicle.