Can I restore a Lion Time Machine backup from a MacBook Air onto a MacBook Pro (currently) running Snow Leopard?
I think the best way to proceed is like this : 


First, see with your IT department to gave you an Mac OS Lion copy (from
Mac App Store or on a usb drive)
Next install Lion and restore with your TM Backup


If you cannot have a Mac OS Lion copy, you can try to navigate to your TM Backup (with a Finder) and copy only what you need on your disk (it depends on what you need to work, if it's just some documents for example it should ok, but I do not recommand to copy an app).