In many communities, there is a well-known practice of changing the tune for L'cha Dodi on the Shabbat preceding Tisha b'Av. But there is an equally old (though less widespread) custom to change the melody on the Shabbatot during the Omer.
This simple but charming air was once common across many European communities. Some have tenuously described it as resembling "Se Vuol Ballare" by Mozart.