Had a similar situation some years ago when my wife BMW 3 series estate was written off by a woman pulling out of their driveway without looking. The police were called as both drivers were admitted to hospital---thankfully with only very minor injuries. Their subsequent reportI apportioned the whole of the blame to the other driver.
I then informed her insurance company that I wasn't interested in their money---I merely wanted a vehicle of similar specification, age and mileage. As the car was a fairly unique specification that was going to be difficult. I accompanied my response with letter from my BMW dealer explaining how difficult it would be to source a similar vehicle and that in his opinion it would cost at least $X thousand pounds. Other insurance company paid out a very generous amount in full within a week without any further quibbles.
It might be worth approaching your Lexus dealer to ask if they would provide a similar letter saying, in their opinion, how much it would cost to replace your written off car.