After your exotic Climbing Lily flower (see link for flower photo) fades you'll see an interesting seed pod develop. The seed pod that a Gloriosa Lilies will produce isn't as colorful or exotic looking as the flower but still is interesting to watch as it develops seeds. Withing a few weeks your seed pod will starting splitting at the bottom exposing round tomato-like fruits that contain the seeds you're looking for if you want to propagate by seeds.
When handling the seeds it may be a good idea to wear gloves as a precaution because all parts of the Climbing Lily are reported to be toxic. When the seed pods on my plants develop I've noticed that the stalks are already on their way to turning yellow or brown and dieing back. At this time I'll gently pull on the stem and see if it separates from the tuber below ground. If it doesn't I'll move the plant to a protected area where it won't get watered and allow it to dry before I lift the tuber for winter storage. If you don't know what to look for below ground in a previous post titled Gloriosa Superba 'Rothschildiana' I added a photo of the tuber to the entry. Once again when handling the tuber it would be a good idea to protect your hands just to be on the safe side. It should take between two and three years for a tuber grown from seeds to reach blooming age.