Rabbit runs

I keep my rabbits in the summer house at the moment. They have a small run attached to their cages. When the weather is nice I put them out on the lawn. The only problem is they leave rabbit droppings everywhere. I move the run often but it means my lawn is a mess. The holes they dig I can fill in. Should I keep them on the patio? Do they need to be on grass? How do other people deal with claring up after them outside? Or am I being too fussy?

How big is the run and their cages?

I don't clear it up, it fertilises the lawn and makes it grow extra well the following year.

Elvis and Ambers cage is 6f x 2ft and is 2 floors. Jake and Violets cage is 4ft x 20in (?). They have a 3ft x 4ft run attached to their cages. Outside they've got 6 or 7 ft x 3ft runs. I do have the option of putting them in a 18ft x 18ft (ish) run but that leaves less for the chickens. Decisions decisions!! The outside runs are moved tound the lawn but are making a mess of the grass.