I had some leftover lemongrass a few weeks ago and I made a killer tomatillo salsa with it... I chopped the lemongrass very fine and simmered it with just a tiny bit of water to soften it, then I added it to the blender with all the other green salsa ingredients. Definitely will do again.
Tisane is another way to go too when you've already made the Thai chicken soup and all.
I make Thai curry paste with mine.
Sometimes I'm more authentic and use galangal and shrimp paste in mine, but most of the time I throw together something like this--
the white parts of 2 stalks lemongrass, sliced thin
1 clove garlic
2 tbsp finely chopped cilantro roots or stems
2 tsp fish sauce
1 slice of ginger 1/4 in thick
1 tsp whole cumin, toasted
1 tsp whole coriander seeds, toasted
1 tsp whole black peppercorns
6 fresh serrano chiles, seeds and stems removed
salt to taste
I toss all of the ingredients into a small food processor or a blender and process into a smooth paste. Sometimes you have to add some liquid to help things along--I'll use water or lime juice, depending on whether I have limes around.
I scoop the paste out in tablespoon sized blobs, freeze the blobs, and put them in a ziploc bag. Then I store the bag in the freezer.
When I want a Thai-Style curry, I put a can of coconut milk in a pot, bring it to a simmer, add one or two pieces of curry paste, and then add the meat and/or veggies I'm using in the curry. When everything is cooked through, I add fresh herbs like basil and serve it over rice.
It's not authentic Thai by any stretch, but it makes a quick and tasty go-to meal when you've come home late from work.