[Avodah] Changing the tune in Lecha Dodi - Revisted

[Moshe Y. Gluck]

R' Ben Waxman:
Someone mentioned to me that according to Rav Shlomo Zalman, every minhag 
has a source. The upshot of that is if something doesn't have a source, it 
is not a minhag. How changing the tune in Lecha Dodi, which itself is only 
500 years old, could have a source, would be hard to understand.
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I seem to remember seeing this minhag discussed in the old Birnbaum
siddurim. Does anyone have one? Can you check and see if it says a source
for it?

KT,
MYG