This preseason report on the Browns QB position mentions KL going to preseason camp as the Browns 3rd QB behind Mayfield and Keenum. The mention of Lauletta is at roughly the 1:45 mark in the video.
As a long suffering Browns fan I'm still enjoying the memories of the Browns renaissance in 2020, it was even more fun knowing KL was part of it on the practice squad.
I have no idea how long Kyle is willing to work trying to break through in the NFL, but being around Stefanski and Van Pelt in Cleveland might help his chances somewhere down the road.
Good luck Kyle!
Go Spiders!