The secret — for some, at least — is to use it for flavoring but not to eat it. Lemon grass is essential in Thai and Vietnamese cooking and is used to flavor curries, soups and many other dishes.
In theory, you peel off the tough outer layers and use only the pale, lower portion of the stems. We have seen number of Asian cookbooks that encourage you to slice the stem very thinly crosswise "so that there are no long fibers to spoil the finished dish." And maybe their lemon grass is so much fresher and more tender than what is available to us that it works. But in our experience, the finished dish is pretty generally spoiled if we leave the lemon grass in. We generally keep it in fairly large pieces so that we can pick it out like bay leaves when the dish is done.
Lemon grass can be pounded into a paste and used for marinades and in stir-fry dishes, but even here you really should grind it to death in a mortar and pestle rather than using a food processor or other cutter in which some of the fibers can survive.