BLACK TRILLIUM, the first of this 5-book "series", was written by 3 cooperating authors, about 3 princesses protecting their country against sorcerers & hostile invasion, with the help of 3 magic talismans. Then the authors went their own ways with individual stories, still set in the World of Three Moons. May wrote BLOOD TRILLIUM and its own sequel, SKY TRILLIUM, continuing the story of all 3 princesses. BLOOD TRILLIUM is set 12 years after BLACK TRILLIUM.
Details in GOLDEN TRILLIUM (by Norton) and LADY OF THE TRILLIUM (by Bradley) contradict details in May's books, but GOLDEN TRILLIUM follows the story of Princess Kadya, and LADY OF THE TRILLIUM follows the story of Princess Haramis. So ... you actually have 3 series here ... all starting with BLACK TRILLIUM, and all of them following the story of one or more of the 3 princesses featured in the original book.