@niamh it's possible, and considering the fact we do have this data point of Lecha Dodi i'd say it's probably the explanation, but it is very much an outlier - my dad's family otherwise kept a whole lot of their original tunes, even when much more common ones are available. as a comparison, the only Passover tune that we don't sing in the traditional tune is Echad Mi Yodea and that's because that one to my knowledge had the common tune overtake virtually everywhere and i don't know of a single person who doesn't traditionally sing the common tune.
and also, even for Lecha Dodi - the tune we sing is an Ashkenazi tune, but not the common one. The common one (at least in Israel) is actually the one written by Zeira in 1952.