Well, it looks like my mystery plants turned out to be (Nile Lily) Agapanthus! I was so surprised because I've been growing Agapanthus for a long time and didn't recognize these as the Nile Lily. Maybe it's my age
These plants were in the ground when I moved here a year and a half ago but they didn't bloom at all last year, probably because they were in deep shade and received no sun at all. I've kept that area pruned of overgrowth of shrubs and they now receive full sun for the first half of the day and one has finally put up a bloom stalk with buds forming:
I can now mark this as solved and close the thread.