Hi,
I have my lemongrass in a large pot that gets dragged in for the winter every year. I have a garden window so I keep it there and it doesn't go dormant. I've read you could keep it in a cooler room and it will go dormant for winter, but I don't have experience with that.
Lemongrass does well in a large pot in full sun outside when it is warm. I have Gerber Daisies in the pot with it. They are a tender perennial for me also. The Gerber daisies have rounded foliage in low rosettes so they make a nice contrast to the upright lemon grass. I did have a sweet potato vine trailing out of the pot at one time, and that looked good also. Look for a full sun tender perennial that stays low with contrasing foliage that appeals to you. Or plant full sun annuals that contrast nicely with the lemon grass and then pull them out for the winter. Then you could do something different every year if your more of a like to try something new every year kind of person.
Remy

I realize this thread is 5 years old, but since I had the same question, it bears a revival. According to Chermarie on Hubpages (http://chermarie.hubpages.com/hub/companionplanting), lemongrass (Cymbopogon citratus) deters many insects, esp. when planted in conjunction with lemon verbena (Lippia citriodora). The ever-powerful Wikipedia lists citronella and a few other insect repellant components in it (http://en.wikipedia.org/wiki/Cymbopogon_citratus), and since the lemongrass I bought from the market has established some nice roots, I'm about to find out if it actually works as an insect repellant. We have some pretty aggressive bugs out here in Okinawa, and I'm always on the lookout for ways to protect my precious "children".