David, I have Lycoris radiata and L. aurea in Greece, in unwatered parts of our hot frost-free garden. Both, particularly radiata, have increased well there, and I think radiata has seeded itself around slightly; I'm never there myself at their flowering time but am told that it certainly flowers.
Here I still have the parent clump of L. aurea which must be about 20 years old now, in a big box of compost under frost-free glass, where it gets some water all year (because it shares the box with allegedly Lilium wallichianum). It always flowers well, and usually sets seed.