Both the bulbils and the small plants can be potted up now. The bulbils are likely too small to be planted out - they'd just get lost or smothered by other larger plants - and the current weather may be a bit too extreme for the benefit of the plants. Use a proper potting soil for the containers, not garden soil. Leave the stalks in place until they dry or wither naturally - this ripening process is what feeds the bulbs to supply next year's flowers.

True lilies do not need a forced chill period and should grow very well in any zone 7 climate. They need very well draining, organically rich soil and even moisture (but not wet) in summer. Sun to part shade in hot summer climates.

The best thing - at least that I've found - to do with the bulbils is plant bunches of them in a pot then plant the whole pot in the ground in an out of the way spot (or at least someplace where you can keep track of it). And you can pot them up now, I wouldn't wait too long as they start to shrivel as the little root grows. Sun/shade conditions don't seem to matter early on as they would normally fall in place and sprout around the parent plant anyway.

The reason I would segregate the bulbils in pot(s) initially is because when they sprout they look almost like a blade of grass - easily lost in the garden setting or accidentally pulled up. Leave them that way for the first season. By the second season, they should start looking like a lily stalk, and even being crowded together in a pot should have reached a bulb and stem size that can be transplanted out more easily. Then they should really take off - I've had some bloom by the third season. They'll be setting their own bulbils in the leaf axils and you'll have tiger lilies forever.