We put 4 x 1's on their side around the opening of the ramp...that keeps "most" of the bedding inside. What does fall out gets cleaned up when we move the coop/run to the new spot. If you put the lino in in pieces you have to be extremely careful about the seams...if an edge sticks up at all, it'll defeat the purpose of easy clean...and you can be sure you'll have at least one nosy bird digging and pecking at it, LOL. Check Craig's List and your local Freecycle...there's bound to be someone around who has a piece leftover who'd like to get it out of their shed or garage

You could also just put several layers of paint on the floor...making sure the top couple were a glossy finish and I'm thinking it would still be pretty easy to clean. That's essentially what ours is. We mix Sweet PDZ into their bedding and it really works great...keeps the poo dry and pretty much odor free. Because it's dry, it doesn't stick to the floor and comes right out with the bedding when it's cleaning time.
We got the last coat of paint on the roof yesterday, so ours is finally done. We didn't paint the inside at all; the outside is the same color/trim as our house and shed and we put rubberized white paint on the roof for waterproofing and reflection of our hot, hot sun here. DH had to re-work the ramp...he'd originally cut it from the floor and hinged it. But that floor is 3/4 ply and it was really heavy to lift and lower. Plus, with the configuration he wasn't able to put the cleats on to the bottom and the girls were having some difficulty getting up and down. He replaced it with a piece of 1/4 inch and made it so the cleats go all the way to the bottom and it works perfectly now!
I'll try to upload some pix later this morning