I think that is a cute idea and wanted mine to be lawnmowers for me! And of course more reasons for adopting But you have to think about a couple of things:
(Some others may not see these as possibilities but I do)

Other animals coming into the yard might have bad bugs in them and they make droppings in the yard and then the buns eat the droppings and get sick

Poisonous weeds hiding in the grass

Pesticides used on the grass by previous owner

Poisonous items put in the yard that haven’t washed away from the yard yet

Some bird dropping may have seeds in them that are poisonous to buns

I love the idea but I don’t know how safe it would be for them but maybe some others have done the same and have good ways to help prevent some of the issues!

Oh I think they’d manage but if you want it done in a more timely manner, definitely hire, oops I mean adopt a few more

Lawn mown grass isn’t safe to feed, the heat in the grass causes it to ferment slightly and it causes stasis.

Rabbits need to be introduced very slowly to grass or they’ll get stasis so for the first few weeks, offer them small cuttings of grass, and gradually increase the amount.

In terms of needing to adopt more… Keep in mind the stress of bonding ?

As for fertiliser it will take a lot of heavy rain to leach it through the soil to be safe-so if its dry it’ll take longer. (keep in mind rabbits will dig down into the soil so you need to give the fertiliser time to get out of it) and after 2 lawn cuts-as fertiliser grown grass contains it (depending on the type of fertiliser-I’m assuming a very toxic one)

I use bunnies and used to use piggies as lawn mowers, we currently have five bunnies, on a 10 m square garden that hs never been treated, it was laid new when we moved in dec 2000.

first thing to be aware of, you will never have a nice even garden. some bits will be cut down to the ground, others left til there is nothing else to eat, ours is only short everywhere now due to the recent heatwave and lack of rain, normally there are loads of tufts that every bun/piggy has turned their nose up at. yes seeds get dropped, by birds, like ragwort. these can be watched out for and removed, but rabbits aren’t daft and wont eat these anyway as long as there is something else nicer to eat, any more that they would in the wild.

regarding the feriliser, I’d leave it over the winter to wash in well, and start the bunnies out for short trips in runs maybe feb. bonding isnt necessarily an issue, ours go out in separate runs in pairs in runs along side each other works just fine and it is easier to move 3 runs around.

hand cut grass cuttings i e using shears or a pair of scissors is ok, i do this in winter. cut well above the ground to avoid fertilizer and like any new food introduce slowly. its the heat from the mower causes the grass to start to ferment

Oh yeah true! And I agree with the above, You would need to make enclosed areas with a top on it for the buns so no predators can come in and grab them, big birds are great at doing that to small animals. It would be a lot of work but they can enjoy outside and help maintain your grass.