Lilys grow from bulbs, which can (and should) be separated every couple of years. They generally grow another part of the bulb onto the original, and eventually can choke themselves out.
After the flowers have died and most of the greenery is dried, but before the end of summer, dig up the bulbs carefully. You can just lay them out and see how many you have, and then can either discard or give some away, or just allow the garden to be larger
You don't have to be super careful, just break apart the bulbs when it's apparent there are groupings. Even if only two, they'll grow healthier if single. You can plant more than one in the same space, but then space the next bulb(s) a few inches away. This will make for a very full and lush area of greenery, even when the flowers aren't blooming.
When splitting and transplanting bulbs, sometimes they won't bloom the next year from what I've heard, although I've never had that problem. Mine always come right back the next spring. Could be that people who didn't get flowers the first year either split them too early, or too late.
