Lino on concrete?

My 2 rabbits have an enclosed wooden run which is connected directly to their hutch, so they have full time access.
Our female is currently struggling with urinary incontinence (and a whole host of other health issues) and lays in the run for a large portion of the day.
I currently have half of the run taken up with a huge plastic litter tray (used underneath plant pots, so very shallow), and the other part of the run covered with absorbent, rubber backed door mats.
The door mats are washed and replaced daily, and the litter tray is spot cleaned several times a day.
The problem is that urine is still getting between the gaps in the various floor coverings, and soaking the concrete.

Can I put a large piece of lino underneath everything to protect the concrete and make it easier to clean?
I am worried that with Summer fast approaching the wet concrete will quickly become very smelly and attract flies.

A single sheet of lino should do the job.

You could also look at stable matting - it's thicker and made just for this sort of use. You should be able to sweep and hose it down. There is also concrete paint which stops the concrete absorbing eg urine - it's often used for garage floors. For example:

http://www.rubbermattinguk.co.uk/index.php?route=product/category&path=67_59
http://www.screwfix.com/c/decoratin..._sp=managedredirect-_-decorating-_-floorpaint

I would think the concrete paint would be an easier option, as with the lino you'd need to seal it around the edges to prevent urine getting underneath.