Gospel is implied to both possess his mom's power as well as a natural immunity to his father's poison (which is the basis for the anti-demon bombs).
For obvious reasons, the CATT fear Lorim and her child, and would probably not hesitate to remove this "threat" if possible.
Zeke works for the CATT (because of his ability), so he's keeping his relationship with Lorim a secret to both prevent himself from being used as leverage against Lorim and Gospel as well as prevent Gospel from being their new No. 1 target.