Can a Paladin use “Lay on hands” on himself?

The question is simple, like the subject: can a Paladin use “Lay on hands” on himself? Won’t the 7-9 option be “weak” in that case?

Well, the move says "When you touch someone, skin to skin..." I think you have to do syntactical gymnastics to see that as anything but laying hands on someone else.

But, someone else might turn the question back and ask "What are the potential costs when a Paladin heals themselves?" And you would have a custom move.

A paladin laying hands on himself would also pretty much negate the 7-9 results where he takes on the wounds of the person he heals.

I would believe no, for the reason that lay on hands seem to lend itself to the selfless nature of the paladin, thus it is meant to help others, the paladin himself can't be healed, furthermore if he could he would invalidate ALL 7-9 and not only those used on himself, since he could just use it on himself until he got a 10+.

You could get an advanced move where the paladin heals himself in a 10+ in addition to its usual effects.

Agreed; the Paladin heals others. It's a selfless thing. But if you want him to be able to heal himself, write a custom move using the Cleric as inspiration. Keep in mind that this sortable blurs the line between the class roles, if that matters to you (it doesn't have to).

I say, to do it, do it.  If you don't do it, you can't.  I totally just did it, as a player, and it wasn't a problem.  I rolled a 10+, so no problem.   On a 7-9, I would have suggested taking weak but healing the HP as I spread my wounds out across my body and soul.  Don't ask, just narrate something cool.

For example, here's what I said:
"My head swimming from the harsh blow of the tentacle and subsequent contact with the unnatural stone altar, I black out momentarily. In my haze, I see my lord's face, his sword cold against my neck, as I kneel and recite the vows of the order. "...to serve and honor. To protect and sustain..." Just as suddenly, the squishy cacauphany pulls me back toward consciousness. Rubbing the salt water from my face, I feel a little better and I know what needs be done."

He'll go blind.

/rimshot