You are right, of course Annie, the lyrics you refer to are from Leonards 1984 album Various Positions. However he did another version on his 1994 album Cohen Live. Lyrics below.
Baby, I've been here before
I know this room, I've walked this floor
I used to live alone before I knew you
Yeah and I've seen your flag
On the marble arch
But this love, love is not some kind of a victory march
No, it's a cold and it's a very broken Hallelujah!
Hallelujah, Hallelujah, Hallelujah, Hallelujah, Halellujah
There was a time you let me know
What's really going on below
Ah but now you never show it to me, do you?
Yeah but I remember
Yeah when I moved in you
And the holy dove she was moving too
Yes and every single breath that we drew was Hallelujah!
Hallelujah, Hallelujah, Hallelujah, Hallelujah
Maybe there's a God above
As for me all I ever seem to learn from love
Is how to shot at someone who outdrew you
Yeah but it's not a complaint
That you hear tonight
It's not a laughter of someone who claims to have seen the light
No, it's a cold and it's a very lonely Hallelujah!
Hallelujah, Hallelujah, Hallelujah, Hallelujah
I did my best, it wasn't much
I couldn't feel, so I learned to touch
I've told the truth, I didn't come all this way to fool you
Yeah and even though
It all went wrong
I'll stand right here before the Lord of Song
With nothing on my tongue but Hallelujah
Hallelujah, Hallelujah, Hallelujah, Hallelujah
Hallelujah, Hallelujah, Hallelujah, Hallelujah