I agree with everybody else but I'll go through the details anyway.
1.Deeper water will just make the leaves spread farther. Shallow water will make the plant more compact with leaves that will tend more to pile up above the surface and crowd together with shorter leaf stems. this might hide the flowers if they are not held high.
Ken landon leaf prunes once a week and says that it makes them flower more and stay very compact , even a plant like mayla.
Small pots with just enough fertilizer to keep the plant growing and green, no more.
Divide yearly so that you will not only keep the number of leaves down, minimizing leaf pile up but some plants make many tuberoids as I call them and dormant crowns. these dormant roots, or stems and crowns as they really are, rhizomes, more than really crowding the plant and making it produce less flowers, what these dormant rhizomes do is demand food since they are not making leaves or food they are basically parasites on the plant, dragging it down.
I believe that these dormant rhizomes and tuberoids also somehow chemically inhibit flowering in nearby crowns that are not dormant since if you fertilize these plants they still won't flower like they should even though they have plenty of nutrients, they are not excessively crowded above the surface because the dormant crowns are not putting out leaves. they are not crowded by roots from the dormant crowns because the dormant crowns don't have roots.
My idea is that the chemicals that trigger and maintain dormancy in these dormant crowns is migrating to the nearby growing crowns and inhibiting there growth and flowering just like the plant normally does in the fall as these same dormancy hormones build up and trigger winter dormancy. Removing these parasitic inhibitors by dividing is one of the most important flower producing things you can do no mater how big the plants are or how crowded they are, either by each other or by a small pot.
I grow my plants in beds in big mud ponds with adequate fertility and complete sun. These plants soon show how they respond to what people call overcrowding because I never divide or thin them. I have noticed different behaviours in different plants. I will try to describe this continuum by dividing it up into three parts , the two extremes and the middle.
One extreme is a plant like Clyde Ikins that very rarely divides or makes tuberoids. A plant like this will show very little negative effects from close proximity to other growing crowns because it makes almost no dormant crowns or tuberoids Very desirable for people who hate to re-pot every year. My Clyde Ikins bed is many years old and is still not "overcrowding " and flowers like crazy.
The other extreme is a plant like Colorado. It produces very many dormant crowns and tons of little tuberoids. within 2 years my bed of Colorado quit flowering altogether,4-5 flowers the whole summer from a whole bed of plants.! Colorado rhizomes grow pretty slowly in my moderately fertile pond and the non dormant crowns can't grow themselves far enough away from the dormancy hormones being produced that keep the dormant crowns dormant and they never flower. I must diverge for a minute and explain something to the people that I can hear in my head saying " I have Colorado and I haven't repoted it in two years or more and It flowers great for me " Tinkster. I have a Colorado plant in a pot that I have not touched in three years at least and it still flowers pretty well. The explanation is this. The Colorado is planted in a pot and of course does great the first year. Then I have to explain what happens next. I have also noticed that when a lily like this is first planted it will rapidly make three or more growing crowns and when a plant like this divides or rests for the winter it makes a whole slew of little dormant tuberoids. These tuberoids, the next year prevent the new crowns that grow from last years rhizomes from growing fast or putting out leaves and roots, as well as slightly slowing the flowering and growth of last years growing crowns depending on how big the pot is and how fertile the soil. A big pot with fertile soil will make a faster growing crown that can get farther away from the nearest group of tuberoids and dormant crowns. less hormones because of distance from the source and unoccupied fertile soil. So if your pot is small and your soil is not to fertile inhibition is high in the second year. If your pot is big and fertile you might get by with another year without repoting. but to make this quicker lets assume a small pot and not super fertile soil. Yet another thing I have noticed oddly enough is that when a plant is in a pot it will grow fast at first then slow down as described, producing many tuberoids. But then when the fastest crown reaches the edge of the pot and escapes and puts down roots outside of the pot a strange thing happens. The crown hits open space to grow and the roots grow to the bottom of the pond and find all of the fertility it needs. This immediately invigorates that crown but none of the others and the big crown grows and flowers like normal, which for Colorado is lots. For some reason this crown will dominate the whole pot and seems to prevent the other growing crowns from growing as fast and escaping the pot. maybe they are just left in the dust of dormancy hormones so to speak. As well as normal apical dominance from this one vigorous crown. I deliberately make use of this trait to create lots of tuberoids and crowns in pots with my seedling plants. then when the plant grows a crown outside the small pot the plant grows to its full potential to meet my judgement. Remember I'm ONLY talking about hardy lilies here but hardies share a trait with tropicals that completes the picture I'm trying to draw here and that is that a hardy lily when highly fertilized does not make NEARLY as many tuberoids and offshoots as a stressed plant. Just like a vigorous tropical rarely produces reproductive tubers. Probably the same thing going on. This adds an even greater inhibition to the tuberoids and crowns still in the pot and there they stay. If you break off the dominant crown, Tinkster, then the crown closest to the dominant crown that was just removed will rapidly replace the crown just removed and continue to dominate the pot. Removing this dominant crown periodically Keeps the rapidly growing apically dominant crown physically close to the recessive crowns and the domination of the dominant crown is enhanced and maintained through proximity.
A third plant type I can describe that will complete the picture even further is a plant that makes lots of tuberoids and dormant offshoots but abandons them after a year or two and lets then die. To me this is the best of both worlds because as a lily seller, in the future at least, I want a plant that will not overcrowd rapidly and stop flowering for my customers, and me too, but will divide rapidly for increasing my stocks for sale. I can't name a plant for you that is like this that you would know. The ones I know of are my seedlings that you would have no experience with. One of these plants that I consider a breeder because it blooms like crazy slowed down it's flowering one year because of tuberoids etc.
Then the next year was back to it's old self. I dug around and discovered that most of it's dormant crowns and tuberoids had died and rotted freeing the growing crowns from their inhibitions.
In number 2 I think you answered your own question. A smaller pot and less fertiliser will make a smaller spread, leaves, and flowers and depending on the variety should still bloom well.
I think I answered question 3 pretty well already. according to Ken it makes them flower more because the plant produces flowers AS it produces leaves. In other words it HAS to produce leaves TO produce flowers, the more leaves produced the more flowers produced and as long as the plant is receiving Lots of light and enough nutrients it will have more than enough photosynthetic area to feed its self and flower well with most of it's leaves removed or at least it's older leaves removed weekly. When you remove leaves the plant says Hey something ate my leaves so it produces more and more flowers along with them. I believe that more light in particular increases the ratio of flowers to leaves produced.
Also fertilizer, especially in certain varieties. My plant Fairy Skirt loves fertilizer and really cranks out the flowers. A plant like mayla will still flower well but will mostly just get leafy.
To summarize, To many dormant tuberoids etc, low light and very low fertility are the main factors that cause lilys to not bloom. Everything else like growing many GROWING crowns crowded together, small pots, and moderately restricted fertility will only make smaller less leafy plants with smaller flowers not less flowers.
At least that is my opinion. And now you know everything I know about the subject I hope that was enough.
