I don't think you can. I think you can only put Young Dragons and Adult Dragons in there. My apologies if this turns out to be incorrect (haven't touched this game in a week, time to get back on and beat it for the 100th time). I'll let you know if this can be done.
I was mistaken. You CAN put baby dragons in the lair. You have to have it in your inventory and not have it as a pet or anything. Pressing "remove" puts it in your inventory.
