NO!!!!!!!!!!!!!!!! Lacquer thinner will turn that nice plastic into mush!!
If you want to strip the paint, try Castrol Super Clean, Easy-Off Oven Cleaner, or Simple Green.
If you're getting too much dust in the paint, try putting the freshly painted item under a bowl or something so that it dries in peace. You might find that a fan will blow more particles onto the paint, rather than away from it.
Another trick is to just lightly sand the paint in between coats. A very fine grit like 600 or higher would be good to just knock off all of the dust bumps in prep for the next coat.
Good luck and keep us posted on the progress!!
Murray