Digging and transplanting is best done when the weather cools down after October 1st and the leaves have begun to turn yellow before digging lily bulbs. While leaves are still green your bulbs are manufacturing food to grow themselves larger for next year. A lily bulb can lose over one its size while putting up a stem, then after flowering, must build itself for the next year's bloom.
This is the reason you should not take more than 1/3 of the leaves when cutting stems to bring indoors. Commercial forcing greenhouses discard bulbs after cutting the entire stem, because if they tried to reuse the same bulbs, it could take the spent lilies 2 to 3 years of additional growing to recover the size and quality of the cut flowers, so it is not cost effective. Stems on lilies for vases at home can be much shorter, click cut flowers for a brief guideline.
When all leaves have turned golden yellow or brown, cut stems down to 5 or 6 inches above ground level before starting work. Set your spading fork or shovel 4 to 6 inches away from the outer stem of a clump and dig down one complete shovel depth, at least 12 inches. Gently work your way around and under the white, pink or purple colored bulbs to easily lift them out of the ground. Bulbs which have put up multiple stems have either divided or produced smaller offshoots called "Bulblets" that are genetically identical to the mother bulb (clone). Gently tease roots and bulbs apart from each other, sorting as you go. Work with only one variety at a time to keep from mixing up different named clones.
With your fingers, clean excess soil from the bottom and sides of larger bulbs. There will be a group of stem roots just above the bulb that may have a few pea-sized bulblets hidden within the cluster; you can use a garden hose to wash off soil to make them easier to find if you would like to save them, but any washed bulbs will need to be "air dried" for an hour or so before planting. Cut the old stem just above the large bulb and discard; stem roots are feeding roots, they grow new each year and are not needed over winter. Any bulblets that might be attached to the old stem can be gently removed at this time.
Plant larger sized bulbs with 4 to 6 inches of soil covering the top of the bulb, smaller ones set about 2 times their size and bulblets only an inch deep. Dianna always recommends that you dig the receiving holes first, and then dig out the bulbs for transplanting. Lily bulbs will dehydrate quickly if allowed set out in the sun or open air for more than a week and an overzealous individual may tire or run out of time to finish the job in the same day or weekend, a good plan for moving other plants as well. Don't take on more than you can completely do at one time.
Lily bulbs from B&D Lilies for spring delivery are dug in winter, carefully packed in large bulb crates with attention given to proper moisture levels, moved to coolers in late November and the temperature is then slowly dropped to mimic a natural winter. This is difficult to achieve in a home refrigerator, the reason why lilies need to remain planted in the garden and do not grow as well if "stored" bare in a shed, garage or fridge over winter. Although the bulbs might not wither away and dehydrate noticeably, their growth potential will be compromised.