Probably because the car already has them fitted, the race cars on the game don’t have a “Race Tyre” option either, because they’re already fitted as “Stock”.
The reason I am asking is because visually the stock tires on the Vanquish LCE have the sidewall design and tread pattern of the Sport Tire Compound. It’s also the only LCE car where you cannot change the tire width.
I did a test comparison where I just quickly upgraded a normal Vanquish as close as I could to the power/weight of the LCE Vanquish with the exception that I added Race Tires. No suspension or drivetrain upgrades were added and the was a massive difference in the grip compared to the LCE. The LCE Vanquish loses grip exactly like you would expect if it had Sport Tires.