The question is what to do with them once those lovely flowers drop off.
The short answer: Keep them!
Kathy Huber at the Houston Chronicle gives a brief answer for how to do this.
The Aggie Horticulture website gives a long answer. They include the history of the plant, tips for choosing a healthy specimen, and detailed instructions for transplanting.
According to Dave's Garden, these bulbs like neutral to slightly acidic soil and are able to survive temperatures down to around five degrees Fahrenheit, which is well below what we generally experience here on the Gulf coast. Most people recommend transplanting these in a sunny location and insulating dormant bulbs during cold weather by mulching. As these plants prefer good drainage, that means containers or raised beds for those of us with heavy, alkaline gumbo soil.
Though we call them "Easter Lilies", Lilium longiflorum is not gauranteed to bloom exactly at Easter Sunday. Very often the ones that we see in the stores have been forced by their growers to bloom at just the right time. But their flowers are just as pretty, regardless of their timing!
*Keep your cats from eating your Easter Lilies, as they are toxic!