Some of us use the 5 gallon cornys for fermentation for the very space reasons you mention.
There are specially modified corny lids available that will accomodate an airlock and stopper.
A racking cane has to be used to transfer the bright, finished beer to another keg or bottling bucket.
Cleaning and sanitizing a corny can be a bit of a pain, too (compared to a plastic bucket).
Still, I find plastic buckets far easier to clean and sanitize as well as to transfer beer (via spigot).
That's why I have two fermentation fridges--as I do 10 gallon batches and can only get one bucket in a fridge at a time (along with one or two cornys, if necessary). If you got the space and dough, get two fridges and two Ranco controllers and you're golden.
By "lagering" did you mean just storing the finished beer at cool temperatures (whether ale or lager), or actually conducting a slow fermentation at cool temperatures, i.e., the process by which lagers are made?