If all you want to do is reduce the grain, I'd shoot dewaxed shellac full strength, then sand the wood with a fine sandpaper, such as P220 in a ROS. Then do it again until you have about three coats of shellac on the wood. What you're doing is filling in the grain with the shellac.
Then shoot your lacquer. If there's too much grain, sand that down with P220 sandpaper and shoot again. You want to do two final coats with no sanding between them.
It's difficult to describe how much to sand. You don't want to take all the finish off, especially in the grain. When you sand after the first coat, you might take more off than when you sand later. The sanding will leave marks in the finish, which I find takes two final coats to cover (no sanding on those two final coats).
You can actually go to a mirror finish with this technique but it takes more coats and more sanding. After the final coat has cured, take some polishing compound and rub it down. But don't do this if there's still grain voids. The polishing compound will get stuck in the voids and will dry white. So your finish will have white speckles in it. Not pretty and hard to get rid of.
Mike