What's the difference between "lonely" and "lonesome"

Solution 1:

There is one sense of lonesome that is unique--lonesome as short for 'lonesome self' in the fixed phrases "on your lonesome" and "by your lonesome," meaning alone.

E.g., "Now why are you sitting there, all by your lonesome? Come on over here."

http://www.ldoceonline.com/dictionary/lonesome

Solution 2:

I don't believe there is a difference, apart from lonesome being mainly AmE. Lonely appears to be slightly earlier than lonesome, but both first appeared around the time of the Pilgrim Fathers and I suspect that usage separated with the dialects.

Solution 3:

In the context of American country music, a lonely person is alone and has no sweetheart. A lonesome person is alone, but has someone, somewhere, whose memory of helps that person persevere through the times of being alone.

A lonesome person has hope, a lonely person, not so much.