oooh, lead paint...... I would definitely try to cover it up. Our hens peck EVERYTHING!!!!!! For some reason they seem especially fond of paint chips. Their outside run has one wall that is the garage exterior and they were literally eating the painted wooden clapboards, I had to buy a piece of thin aluminum (sold as roof flashing) and nail it to the bottom couple feet of the garage outside wall, to keep them from eating the paint. Inside, if you scrape off the peeling paint and prime it with a good quality primer, you could probably get away with just repainting with latex. Or maybe buy or salvage some el-cheapo thin paneling or luan plywood to cover the old painted walls?
Good luck and have fun!
Stacey