Should lemongrass be edible or just a flavoring?
If you actually chop it finely, you should be okay. Specifically, you should cut it into thin disks against the grain first, so that you're cutting the fibers into short enough lengths not to bother you. Depending on how tough your lemongrass is, you may have to remove some outer layers to do this.

At that point, it may already be possible to chew, but further chopping should make sure of it. If the pieces are small enough, there isn't really anything to chew, and it's not too likely to stick in your mouth given that it's mixed in with plenty of other stuff in the dish.

That said, there's some variation in the toughness, and it does take a reasonably sharp knife to do this if the lemongrass is on the tough side, to the point that it might not be possible. So if you have issues chopping it finely (or too little of the stalk is tender enough to do so), falling back to your usual approach of infusing it into things is the way to go.