I tried to find some references that connect the longobards with long-bearded axes. I didn't find any (what actually doesn't mean much).
What i did find was the article "Langobarden" in "Reallexikon der germanischen Altertumskunde". Available online here:
http://www.archive.org/stream/realle...e/122/mode/2up
There it is noted that the origin of the longobards based on a long bearded axe is extremely unlikely. (I don't want to translate the lengthy reasoning behind this). This thesis is substantiated by archeological findings that at langobardian burial sites mostly swords, lances, arrowheads, and shields were found .
Best Regards,
Thilo