Amaryllis. I kept one for years by letting it die back naturally after blooming - which took what seemed like a very long time - eventually cutting off all the foliage and putting the bulb back in its box (or any box) in a cool dry place over the summer and into early fall. I've always stopped watering once I put the bulb in storage.

Store the bulb for a minimum of 6 weeks, then plant and start watering again.
After the six weeks of storage, you can remove the bulb whenever you would like to plant it. Replant bulb about 8 weeks before you would like it to bloom.

It is probably Amaryllis. Has nothing to do with true Lilies. You might want to visit Amaryllis/Hippeastrum Forum if you have specific questions or just google for Amaryllis care.

Thanks. Link seems to be quite useful.