This is what solved mine from Lexus customer services
Remove vehicle from the Lexus Link+ App account, via the app’s “My Garage” page.
Sign out of the mobile app.
On the App’s log in page – Choose option to reset your password.
Note: Your must enter your Email/Telephone number, before you get the ‘reset password’ option.
Note: Please change your password to something different from the previous password.
Turn on the car, and log into your Lexus Link account via the Multimedia system by using QR code when prompted.
Scan the QR code shown on the MM system into the LexusLink+ App (My Garage, Add Vehicle, Use QR code).
Once you are logged in to the Multimedia System in the car, please access and enable “Link profile to Key” – an option found under:
Settings (from the Multimedia home screen)
User account (Click into your name on the top left)
Personal Info
Enable ‘Link key’ (as per screenshot below)
This should be a successful prevention of the profile log-out issue. “Link Key” means the MM systems seeks your profile details from recognition of the Key, rather than your mobile phone. The key is a more stable solution for profile recognition.