Lilies resent being disturbed, so replant them as infrequently as possible. If you absolutely have to move them, wait until after their growing season, preferably when they are dormant.

IME, lilies do not mind being moved at all......I've done it many times and they have never blinked!! Like most bulbs they are extremely tough. But you do want to do so when they are not in active growth - at the end of the growing season or when winter dormant. I have actually moved and planted them in the growing season, and if done carefully, the are just fine.

And I would not consider the container planting being too close. Lilies increase or naturalize by producing offsets and the offsets form and grow right next to mama bulb. Eventually the bulbs and their offsets could fill that container but you still have a long way to go before that happens!! And containers look better with dense, full growth than if too sparse.

Well, you have to disturb them to separate the bulbs. If you don't, you get one bulb-clogged piece of soil. That has to be done every few years, and of course should be done when dormant.

I think I will pull up some of my lilies after blooming. When dormant, I can’t see where they are. I had the bright idea to plant lilies and roses together, hoping roses would serve as support. While roses were of the shorter varieties, they quickly became taller than lilies and reality wasn’t quite as my vision. So, I will move the one around the roses (ouch and danger of damaging roses). As I write this, I might just let roses suffocate lilies and buy some on sale. Depends on my energy level in that particular day.