In research with Hemerocallis lilioasphodelus floral induction was started ten days after the end of flowering. In the particular location flowering ended on June 21. That means the growing point starts to change from being vegetative and producing only leaves to being reproductive and producing the scape almost a year before the first flower on the scape opens.
That would be the situation in a location and growing conditions where H. lilioasphodelus does not rebloom. However, it is likely that there are locations and conditions under which it can rebloom (seedlings of H. flava, the older name for H. lilioasphodelus can rebloom).
There are modern daylily cultivars that can rebloom three, four, perhaps even more times in a long growing season under the appropriate growing conditions. Indoors, under grow lights some daylilies can rebloom repeatedly on average approximately every 60 days. Since the growing conditions indoors were probably far from optimum I assume that outdoors in the appropriate locations and growing conditions they may be able to rebloom more frequently at shorter intervals.
One year I divided a clump into single fans early in the growing season. When some of those single fans then later produced a scape I removed the scapes as soon as I saw them. Some of those fans then produced a second scape later. I attributed the first scapes to the normal scapes for that cultivar. That cultivar had never rebloomed here (and has never rebloomed since). I attributed the second (rebloom) scapes to reproductive meristems that had started development before I divided the clump and that did not enter their normal rest period because I had divided the clump.
