There's a great article here that could answer it better than I ever could. Although it's more than just Japanese mythology:
http://ladymaggic.podomatic.com/entry/2008-05-25T03_23_02-07_00
~origamifolder.com
water lily
The Japanese word for flower is "Hana"
Monet painted the Japanese bridge over his water lily pond a number of times between 1889-1890.
In Japanese, Tiger Lily is called "トラネコユリ" (toranekoyuri). The term combines "トラネコ" (toraneko), meaning "tiger cat," and "ユリ" (yuri), which means "lily." This name reflects the flower's distinctive appearance, reminiscent of a tiger's markings.
.water chestnuts .seaweed .algae .bamboo .lily pads .lotus .japanese iris .dwarf cattail
The peacock feather or the lily flower are often associated with Hera, the queen of the gods in Greek mythology. The peacock feather symbolizes her pride and regal nature, while the lily represents purity, femininity, and motherhood.
黒百合 /ku ro yu ri/ means black lily in Japanese.
The Japanese word for lily pad is "ハスの葉" (hasu no ha). "ハス" (hasu) refers to the lotus flower, which is commonly associated with lily pads. In a broader context, "スイレンの葉" (suiren no ha) can also be used, as it refers specifically to water lilies.
The words night lily are said in Japanese as yoru yuri. These words are said in Italian as notte giglio.
'Dancing lily' translates to踊ã£ã¦ã‚‹ãƒ¦ãƒª (odotteru yuri) in Japanese.
Small Lily
The water lily leaf does not have a special name. It can be referred to as a "water lily leaf' or as the leaf of a certain water lily species.