No, lily of the valley is not considered a true lily (lilium).

Lily of the Valley has been placed in the Family: Ruscaceae
Genus: Convallaria
Species: C. majalis... and the common ones we have in our gardens tend to be Convallaria Majalis var. Majalis.

Transplant lily of the valley in late summer or early fall. Although they can be transplanted successfully anytime after blooming, fall transplanting produces hardier plants and increases next year's blooms.

Despite their rampant spread, transplanting them successfully is not always as easy of you might think. Dig deep and be careful not to damage any of the roots. Plant them in their new spot at the same depth they were before.

I like to dig and trade mine as soon as they emerge in the Spring. I have done so for a couple of years and no-one has complained. One suggestion, if you know when you are going to dig them, heavily water them 24 hours before doing so. They will transplant much better that way. I THINK--not absolutely sure--fertilizing them (with water soluable fertilizer) at the same time could give them a boost before transplanting. Or, when transplanted. Good Luck.