There are some lily species that produce stems that tend to wander in the ground before they emerge. Rather than shooting straight up from the bulb, they will veer off diagonally or even horizontally for a while, and emerge from the soil a distance away from the bulb's location. One reads about how they also produce bulblets along the way. Though I don't recall any author actually claiming they produced more bulblets than a normal straight up stem, I always had that idea.
My experience at least, hasn't really born that out. I grow four species that can do this: Lilium lankongense (most of the time), and not uncommonly, L. davidii, L. leichtlinii and L. maculatum. In fact every time I remove a non-vertical subterranean lily stem, I look especially for this trait, and have never found even the slightest increase in bulblet production. That is, until this year with one stem of L. davidii. I thought it was so interesting that I took a photo, not even thinking that I might ever post it. (Aren't you all the lucky ones...)
Bulblets were larger than normal, too. I wouldn't even call them bulblets had I not known of their origin.
I can only speculate why a bulb planted on its side might produce more bulblets, but I wonder if that might only be true for those bulbs that normally produce only straight up stems, and the disorientation of the stem so triggers the production. A worthy experiment.
There are a few species of crocus that naturally grow their bulbs sideways. But those aren't even true bulbs; they are actually corms. I have no idea if it relevant to this discussion, but I'm just sayin'.
