When you write lane do you mean lawn? If so, to go low maintenance I'd get rid of the lawn, but it's up to you. I don't know a way of getting grass clippings out of the stone, but you could use a mower that collects the cut grass to stop it getting into the stone in the first place.

I agree with Beattie if you want low maintenance get rid of the grass (assuming that is what you meant to type).

Mowers without a grass box and strimmers will both make grass go over the gravel, even more so if there's no edging seperating the lawn and stone. I used to have a similar problem when trimming hedging, the cuttings would cover the gravel and make it very hard to clear up. So I simply laid a piece of lightweight material over the gravel to catch the mess and then all I had to do was fold the material up, lift off and empty (or throw away). Made an awkward job very easy!

I agree for low maintenance you cannot have both get rid of the stones or the grass?
Are you letting the grass grow long between mowings? I have an area I dont want grass on and use a mower with an inbuilt grass collector and mow every 3-5 day then use a yard brush to sweep over the stones and with regular/frequent mowing I find there is very little to cover the stones?