They are just really tall lilies that get between 4 and 8ft, not actual trees. I have a few of them and they typically split into 2 each year, doubling the production, sometimes creating small bulbils.

I'd suggest you look at a magnolia tree. There are a wide variety of types and sizes and suitabilities for different climates. Depending on type, they are sometimes referred to as tulip tree, banana tree, star magnolia, saucer magnolia or lily magnolia. I'd suggest a lily magnolia immediately, however their flower color tends to be primarily in the pinks and purples. There are lots of white flowering types as well, many that produce somewhat lily-shaped flowers (even if not specifically referred to as that), so you have a lot to choose from. Most good garden centers will carry a decent selection at this time of year.

How about a white dogwood?