This is a pic from the bottom basically. The long stems to the right of it is the main big partWhat are we looking at?
Most lilies produce a long tuber or bulbs and can be divided when big enough. Normally you let the plant grow for a few years and then dig it up when they go dormant. Look for bits of tuber with a few leaves or leaf buds and separate those bits of tuber from the main piece. Replant them and see how they go.
Be careful when handling or cutting tubers because they can get crushed or infected and rot. Then the plant dies.