Joshua, you can set several pods of several different crosses on the same plant. I've done 5 or 6 pods quite a few times. Most of the time I've made each cross with a single pollen per pod, but there have been times I've used as many as 4 or 5 different pollens as a mix on the same flower. Growing all these seed pods does not harm the plant. When the plant senses it's carrying a good amount of seed, it responds by taking up extra nutrients and it keeps growing longer in the season to compensate, often staying green until frozen late in the season. About the only difference I notice with the plant is there won't be any increase in bulb size with little or no stem bulblets and offsets being formed and sometimes a couple less buds the next spring.
No, lilies don't need to take a rest every other year when seeded. I have one with a 20 plus bud count and a nice inflorescence and I work the heck out of that one every year as a pod parent.
Besides hardiness and a pretty flower, some of the things that are important in breeding is obtaining good overall balance and proportion of the plant. Every feature must not only compliment each and every other feature but compliment the entire plant as a whole. And to carry all that it must have a stiff stem. We can discuss individual features like bud count and pedicel placement, inflorescence form and height, leaf styles, lengths and distribution can all be discussed later as well as some things I may have forgot to mention, I'm sure. You ask good questions, Joshua.