I'd love to help you, but I haven't heard the song myself, and I can't identify it from this list at Jez Lowe's website. Any idea what the title might be? Or what album it's on? Or who else besides Jez Lowe might have sung it or recorded it? Or can you remember where you heard it? Can you quote any lyrics at all? I'm pretty good at finding things, but I need something more to go on.

It seems the word "Hallelujah" doesn't appear at Jez's website at all, and Leonard Cohen is mentioned only once. ("The Parish Notices" is said to be "so sad that even Leonard Cohen was depressed when he heard it.")