In my experience, it's never too late to put manure on a veggie garden. My father always had a load dumped onto our garden mere days before we started our garden (tilled it in), and we always had a great garden.

Can't help you on the rabbit manure question, though.

You might look for pet stores (PetSmart, etc.) that sell bunnies. They clean the cages daily and might let you take the shavings/manure that they toss.

Anyone who raises rabbits as a hobby would also be a source. You'd just need to put a note up on the bulletin board at the supermarket, community center or other public spot.

I have a pet rabbit and use the soiled bedding and manure directly on the plants. It is a non-burning manure and doesn't need to be composted before using.

Just a word about combining high nitrogen fertilizer like manure with lime - I've done it and found out the hard way that it can cause chlorosis.

I'd only apply lime if a soil test shows that you really need it. I'd also avoid turning the lime under if possible, just apply it to the surface. I lost a fairly good sized section of seeded lawn doing that one year - and I had used very well-rotted manure.