You're right, once you have your eye in you can tell an asiatic leaf (narrow, grassy, lots of them) from an oriental leaf (broad, glossy and relatively few in number) every time, as well as from those of a trumpet (narrow but longer, larger and less numerous than an asiatic).

Some other lilies also have bulbils - that's how L. bulbiferum get's it's name. Others will produce them if the stem has the flower buds removed before they open - useful for propagating something.