I move them all to this one section of my island with bamboo and green mums. I have too many now though and they're just building up and yet I can't bring myself to sell them.
I've only ever gotten one because I went through the effort to make my island considered perfect, and then once it was and I unlocked the gold watering can and got 1 lily of the valley, I changed some things on my island to make it more how I wanted (I think the game is picky in annoying ways for that rating) so it's not considered perfect anymore. lol
My one lily spawned in a place I really like, so I have never moved it. I see it as a fun reminder of the time my island was temporarily considered perfect. It's sitting on the edge of a cliff that overlooks this kinda hidden Asian-themed relaxation area that I made next to a waterfall.