Lemongrass is a perennial that's only hardy to zone 9. So, here in zone 6, if you want fresh lemongrass, you got to grow it as an annual or grow it inside. Indoor plants never survive my neglect, but in order to get the most of my plant, I dry the leaves so that I can have herbal lemongrass tea throughout the winter. Being caffeine-free, this tea can be enjoyed all day, and the dried leaves don't have the bitterness that plaques steeped fresh leaves.
Heat oven to 200F.
Cut the leaves so that they fit on a cookie sheet and lay them out in a single layer. You can also dry the stalks for use in soup, but try to put them on a separate cookie sheet because they'll take longer.
Dry leaves in the oven for about 2 hours. Stalks can take 4 or more hours. Leaves are done when they sound and feel like dried hay, and their color has dulled. Dried stalks can be stored in an airtight container as they are. Chop leaves in a food processor or blender but keep the pieces big so that they don't pass through a steeper or fine mesh sieve.
Store in a mason jar or other air-tight container. When you're ready to steep, use about 1 teaspoon per cup (8 oz) and steep for 10-15 minutes. Customize your own flavor by steeping with black or green tea but reduce steeping time to 3-5 minutes. Taste great on its own or with honey or sugar.