The reviews of some of the winter type shoes that I've seen do say the the sizing already takes the need to layer socks and roominess into account, so its likely that a 39 would be very, very large on a 37 foot... (and I almost found out the hard way that unclipping with shoes that are to big can be near to impossible - your foot turns in the shoe instead of the cleat turning out of the pedal!)
From my own experience Lake shoes already run very large. A 37 mt shoe felt 2 sizes to big!