If I remember right, you need to talk to Rhea and company before they leave then head into the Depths but leave without killing the Gaping Dragon and explore a different area. Lautrec should offer it upon returning.
If he asks you once and you say no, he won't ask again. You need to say yes each time, even if you don't have enough souls.
But you're on NG+ or a new character? He should ask so long as you've spoken to Petrus and Rhea then wait for Petrus to come back from the tomb before Lautrec leaves firelink. Talk to Petrus then talk to Lautrec.
I don't THINK you have to have rescued Lautrec from the parish for this to work, but it couldn't hurt.
Is there something about the way I type that makes it sound angry? Maybe it's just something about the way you read.