Found a few Gloriosa Lily plants growing on some abandoned property. When can this be dug up without harming the plants?

Yes you can. Gloriosa Lilies grow from tubers that are usually dug and stored during the winter. If the plant is currently growing or blooming your may want to wait for cooler weather, so they will have more time for the tubers to grow and store energy.

Yippee, thank you @Horntoad , I will wait until the weather changes and the blooms fade. I'd better go out there and put some kind of marker so I can locate them in the future. Thanks a bunch.