They can be planted in either Spring or Autumn. I live in Arkansas, which is not that much different than Texas. I usually buy them in the Spring and plant them then, because that's when they're for sale in the garden centers. Though I'm currently waiting for the ones I already have to go dormant so I can dig them up, divide them to give them more room and pot them back up in fresh soil before winter gets here.

These plants love fast draining soil and full sunlight. I keep them well watered and never let them dry out. I suspect that this might have been the problem with yours. They don't mind the heat, they just don't like drying out. Mine seem to bloom during the hottest time of the year. Smelling their fragrance filling up my backyard garden makes the scorching hot summer weather worth it. Not to mention the butterflies love them, too. If/When you plant some more Oriental lilies, just make sure to keep them well watered in a fast draining soil, with plenty of sunlight, and they'll take care of the rest. :)

None of my friends living in the south had luck with oriental lilies (I used to live in Texas). They generally don't do well in hot and dry zones, though some people have success as reported in the previous post. Orienpet lilies might be a good alternative but orientals are also so beautiful that I think it's worth trying. I think planting them in either spring or fall is fine but since ideally the soil temperature should be in the 50s for their roots to develop, my guess is that very early spring, after the soil had enough time to get cold in winter, could be the best time for Texas.