Lawn care and bunnies

I have a rabbit who needless to say loves grass and I want my lawn to be lush and green not only to satisfy his hunger but also so I can enjoy it. I moved into a brand new house 3 years ago when I had the lawn laid. I had asked for top quality turf but it seems that a cheap turf was laid to cut costs. Since then the lawn has deteriorated badly. It is full of weeds and is dead in places with bare soil showing. I am mowing it once a week and it is definitely not over grazed by the rabbit as it is a large area. I have tried scarifying it and applying seed but this has not helped in any way. I am unable to use chemicals because of the rabbit so wondered if there was any advice anyone can give me that may help. I have considered watering it every day - will this make much of a difference or will I be wasting my money? Any advice gratefully received.

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