Actually, a lot of people cross these two breeds!

However, they are virtually always bred for working purposes - not to say that they don't have good natures and make a nice, but energetic family pet. (The sensible traits of the Border balance the 'hardness' of the Lakeland - Borders are notoriously slow to start working, whereas Lakies can be very headstrong and get themselves into trouble when underground.)
I would suggest that you look in Countryman's Weekly, there are often pups advertised there.