Lorca has obviously some reputation. His previous ship being destroyed, his crew lost might be as far as that reputation travelled - hence him being a survivor. The blowing up part might be where the devil is.
If Lorca is smart enough to suspect Ash is a spy why take a spy back with you?
Edit - mickmike, thanks for the re-watch report![]()
No worries

Lorca was using Tyler to escape. He knew that the Klingons would want a spy on Discovery, so they would need Lorca to escape. If Lorca tipped his hand and killed Tyler, then he'd probably be put in solitary confinement and tortured continually until he gave the Klingons what he wanted. It was a necessary evil. Further on down the line. Lorca could also use Tyler to feed false information to the Klingons or once he's revealed gain intel from Tyler on the Klingons.