Laziest/Quickest way to smooth a wood-grain-textured door?
If it's the same door I'm thinking of, I don't think two coats of primer will do it.  You'll need an actual crack filler.
Bear in mind, if they're flat/slab doors, you can fully replace them with a luan veneer door pretty cheaply.  Something like $45 per door last time I bought them.  Not too far from the price of paint.
Is the fake woodgrain so ugly that a nice coat of paint won't dress it up ok?