Lie angle is angle between the shaft and the sole of the putter. Under USGA rules it must be less than 80 degrees (USGA Rules Appendix II 1.d.(i)). A larger angle creates a more "upright" club, and a small angle may create a "flat" lie. 70-72 degrees is very common in modern putters. Older putters tend to be more upright at 72 or more degrees of lie.
Using a putter with a lie angle not suited to your setup and swing can result in putts not going on your intended line (more on this in an upcoming post). Fortunately, most putters can be bent to custom fit the lie angle to the golfer. Ask a clubfitter or the manufacturer for more information.