I have a 2017 IS200t F Sport for reference.

I use remote start using the Lexus Enform app. The car shuts off after you unlock the doors and you must start the car again once you're inside. I was wondering if it's possible to have the car not shut off?

 

Nope, that is the way it is designed to work.

 

It does that for safety and limiting emissions. The app will run the engine on for 10 min before it shuts off.