Spring is the best time to plant most bulbs, but Tiger lily flowers are so hardy that I've planted in early summer while the weather was still cooler, with great success. I've even separated and transplanted lilies in the middle of summer and although the transplanted bulbils didn't bloom that year, the leaves stayed green and I got flowers the following year.
It's important to give the transplants plenty of water but don't keep the soil wet.
Keep in mind that it may take up to five years before the newly-planted bulbils flower. This article may help you: https://www.gardeningknowhow.com/ornamental/bulbs/lily/tiger-lily-care.htm