Lily bulbs do not like to dry out so taking them out to store is not really good for them. If you are going to repot them then the best time is when they are dormant, ie when the leaves have died off.

Then I would plant them either in a bigger pot, or in the ground. While they have leaves, though, feed them regularly.

welcome to GoY.
if you want to use the pots for something else then yes transplant them into other pots and keep watering and feeding until the foliage starts to yellow and die off. put them in a place where you will remember them but wont spoil your display of other pots.