I do agree with all those that have responded to your questions however it is still an option as you have plenty of shed space. I am in a very similar situation to yourself with not much spare land at this time of year and what we have is very wet.
We lamb from December onwards and can easily finish lambs inside. As yourself I have access to plenty of shed space.
The key is plenty of space and keep them dry. The lambs, and ewes for that matter will inevitably get dirty, or greasy in the absence of rain to wash it out. As far as disease is concerned, touch wood, we don't have any problems. Orf is kept at bay by allowing free access to rock salt and Life Line buckets. Lambs are offered adlib pellets from about 1 week old and they always do well. Unless you feed the ewes well they will lose quite alot of weight in a short time so you probably won't save any money on that side.
The big benefits for us are quick finishing lambs, no poaching the grass so we have a nice spring bite and we don't get ewes with sore teats like we would if they were out in mud, so don't get mastitis problems.
It can work!
John