In my limited experience with lemongrass (which I buy fresh-ish in plastic bags from the fridge of my local asian supermarket - not frozen or dried or anything), it's hard and impossible to chew, no matter how long you cook it for. I usually smash it, split it down the middle and add it to soups or other dishes with a lot of liquid, then take it out at the end like a bay-leaf.  However, I've recently seen recipes in which finely chopped lemongrass is put straight in a stir-fry or a sauce, which just seems like a good way to end up picking bits out of your mouth to me. Is there a problem with the lemongrass I'm buying? Is it that only the green is hard and inedible? Or am I cooking it wrong? 
You're not missing anything, lemongrass is very fibrous and often it is a good idea to remove it like a bay leaf. If it's quite fresh it can be left in if you peel away the outside layers, you use only the most tender portion (about a half-inch from the root to about 2 inches from the root), and you mince very finely. If you do all that, you can stir-fry or otherwise cook lemongrass, and keep it in the dish without causing your guests to spit it out.  There is no harm though in removing it. 