This is short for "lending me your shoulder to cry on," meaning to provide emotional support for someone in distress. Your text seems to have this be almost literal as well as figurative.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
HUBLOTDoes Thanks for lending me your shoulder mean "Thanks for giving me some help"?Specifically, for giving her a 'shoulder to cry on'. http://en.wiktionary.org/wiki/shoulder_to_cry_on