As an update, the dealer gave me a bunch of excuses why I should install an aftermarket remote start that "all their salespeople have on their own cars" instead of Toyota Part PT398-60160. I assume it a cheaper part that is easier to install. I told them I specifically negotiated the Toyota Part and did not want a non-Toyota part. The aftermarket part apparently has an app and features beyond the factory part, but I have the factory remote start on my other LC, I know its limitations, it does what I need it to do and it is dependable.
The dealer told me the part was not compatible and then I was told the part is on backorder and it would take 30 days to get. Fortunately, Eric Sarjeant direct messaged me confirming that even though it is not published that the part is compatible, it is compatible and he had installed it successfully. With this confirmation, I told the dealer I wanted to move forward with the install. I guess the part was not on backorder, because is arrived at the dealer in less than a week.
When Eric Sarjeant direct messaged me, he also offered to provide instructions or a video to help with the install. He ended up sending me a video covering the programing that needs to be done and the need to cycle it several times if it does not take. I tried to upload it here, but I cannot figure out how to do that. If anyone needs it, message me and I will email it.
I cannot express how helpful Eric Sarjeant has been with this issue. I wish I could buy and deal directly with him and his dealership.