Nah, googling it I see quite a few curries that contain lemongrass. I guess I’m only used to it in tom yam. I don’t recall many, though, where I’ve had to put aside the nonedible pieces.
The lemongrass is ground with a mortar and pestle to form the base of many Thai curries, including the most well known red and green curries. So that would be why you wouldn’t have to put aside the nonedible pieces–they’ve all been pulverized to a smooth paste. It’s not a universal ingredient in Thai curries–I’ve definitely had masaman and sour curries that did not have any detectible lemongrass flavor–but it’s pretty standard.
See? I’m not a cook. I just eat the stuff when they set it in front of me and never ask what’s in it. 
Next time you’re in Patong go and see this lady, Pum. She’ll teach you the fundamentals, using all-fresh ingredients - it’s great fun to do and to eat. Her restaurants are fantastic, and she’s an amazing person.
Getting back to curry, norinew, have you ever been to Penzey’s Spices? The nearest ones to you seem to be Rockville, MD and Pittsburgh, PA. Or, you can order on-line here. (Their website also has store locations.)
At their stores you can sniff any of the spices they have, which is hundreds, to see if you like them. We have several of the curry selections but I am partial to the ‘Sweet Curry’ in the small 1.1 oz jar. It is great to sprinkle on turkey sandwiches, eggs, etc. to add a mild kick. (Plus it looks pretty with a golden tan color.) Much better quality than is available at most grocery stores.
The advice people have given on how to use it is great, but don’t be intimidated by any complications before you get addicted to the flavors. Madhur Jaffrey’s cookbooks are stunning, but more often than not I open up the one I have, get overwhelmed by the complexity of the recipe and give up before I start. Her other books may be simpler, but the one I have is usually too difficult for my lazy and impatient self. I’ll have to look for the one dwyr mentioned.