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I suspect insects are eating them or rabbits. Here are articles that should help:

https://www.gardeningknowhow.com/ornamental/bulbs/toad-lily/toad-lily-care.htm

https://www.gardeningknowhow.com/ornamental/bulbs/bgen/protect-flower-bulbs.htm

https://www.gardeningknowhow.com/plant-problems/pests/animals/chipmunk-control.htm

https://www.gardeningknowhow.com/plant-problems/pests/animals/get-rid-squirrels.htm

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

https://www.gardeningknowhow.com/plant-problems/pests/animals/keep-rabbits-out-of-gardens.htm

Divide away! I didn't know if you meant true lilies, daylilies, calla lilies, etc., so this publication covers dividing all the different types of underground storage units, such as bulb, rhizome, corms, tubers. There is a diagram of the bulbs, but explains how to divide.

https://web.extension.illinois.edu/bulbs/bulbbasics.cfm

Full sun and avoiding overcrowding are two things they need. Does your stand look crowded? It just may need to be divided. I find deadheading helps, too.
According to the Daylily Society, they benefit from fertilizer in spring but isn't necessary every year.

Here is more:

https://www.gardeningknowhow.com/ornamental/bulbs/daylily/no-blooms-on-daylilies.htm

https://daylilies.org/daylilies/faq/

Many lilies need a winter dormancy. If they did not receive one, then this could be the problem. Soil fertility issue could be the case, as well. Make sure that you feed the container grown plants a few times per year, or at least once per year.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm

https://www.gardeningknowhow.com/ornamental/bulbs/lily/planting-lilies-in-containers.htm

The leaves of bulbs naturally fade over a period of time while the bulb is regenerating for next spring. You can plant it outside or if it is getting enough light indoors, you can let the foliage die, then store the bulb over winter in a cool place like the garage before bringing it back inside in the spring. Here is more:

https://www.gardeningknowhow.com/ornamental/bulbs/bgen/bulbs-to-grow-as-indoor-houseplants.htm

https://www.gardeningknowhow.com/ornamental/bulbs/bgen/forced-bulbs-in-pots-yearly.htm

It's your choice. Some people leave the foliage to protect the plants from cold winters, however, then pests and disease can overwinter in the dead leaves. But, if you garden for butterflies, you want to leave the foliage in case you have overwintering butterfly eggs, pupae, or adults. I sometimes will cut things back, but put the stems in a corner of the yard in case there are chrysalises.

In the case of lilies, you should let the foliage die back before removing those leaves. That is how the bulb is regenerated, just like tulips and daffodils.

Some people don't like the untidy look and will cut everything back in fall. I wait till spring to do most cleanup because I have butterfly host plants.

https://www.gardeningknowhow.com/garden-how-to/info/cleaning-up-garden.htm