If it was just on the surface I would say brake parts cleaner but because it's a bleed thru you may have a low percentage of success. I agree that I would recreate with some scrap liner and try a few of the suggestions offered first.
I used "K-Grip" in an aerosol can which the Fiero Store sent me with the liner material.
I didn't have lighter fluid, but found some Goo Gone and dabbed the surface with it. I had some mild success, in that it can still be seen, but the stain is no longer white and crusty. I'll have another go at it, and it if proves to be unsuccessful, I'll try some of the other remedies mentioned.
My Carpet Cleaner guy uses "Brake Cleaner" to get out nasty stains. I've used it before on my upholstery to spot clean grease. May not have any affect on glue, but as stated try it on a piece of scrap first.
The factory and replacement fabrics for headliners is pretty fragile. I doubt your going to get any passable results with anything. The fabric is very porous and fuzzy. Its almost impossible to even get some mild dirt out of it without rubbing down the nap or discoloring it. I detail cars, and light color headliners are a nitemare to mess with and seldom look better after. Wish you good luck though. Best chance is patting...and NOT rubbing at all. Even my professional upholstery cleaner machine cant do anything with them.