Well I am not saying that there isnt a problem but, I just thought I would mention that Lawnmower blennies dont swim all that well they lack a swim bladder so they dont float like most fish. and mine rest on his side with his fin kinda propping him up. I thought there was something wrong with my blennie for days after I got him because of their strange swimming and resting behavior. Also he has always keep his mouth open more often then not. But he is the happiest healthiest blennie I can imagine!
Is he laying completely on his side?
How is his breathing?
How new to your tank is he and is this different behavior then he has been displaying?
What are your water paramiters?