I have some tree lilies in large pots. They will be fine just like that, at least for a few years.
I normally feed occasionally with tomato feed when they are growing.
It will prevent the plant from wasting energy if you remove the seed heads from where the dead flowers are. But don't cut down the old stems while they are still green. You should let the foilage die down naturally. Always be vigilant for signs of the red lily beetle, or its sticky black lavae.
You can leave the pots outside, if you want to. If the pots are easy to move, then bringing them under cover during the Winter may prevent the pots from being damaged by frost. The lily bulbs can tolerate very low temperatures, though they don't like excessive wet during the Winter, so bringing under cover can reduce that. I've had some pots of lilies, which were too heavy to move, left outside all Winter.
You mentioned moving the bulbs into soil. Growing in soil does have some advantages for tree lilies. Although a 12 inch pot is large enough for the first couple of years, the plants will get too big for a pot of that size. So you'll need to upgrade to a pot of around 17 inches. Or you can put them in the soil. I have a clay soil, so lilies won't grow well in that, so have to use very big pots.