It seems as though their entry into the US took a great deal of time and effort. They probably had no desire to travel outside of the US once they arrived. So no passports?
Are they still citizens of Lao? If so, could you reach out to the Lao embassy? I am not well informed so just an idea. Perhaps if they left Lao during the 60’s or 70’s could they be not in good standing with the government?
They will need passports to travel. The Thai government will determine what visas they are eligible for based upon the passport. I think that this situation requires informed help. Perhaps they could apply for US citizenship.
We should always include what type of visa and or extension of stay we have in our original postings. It will hopefully get us better if not fewer responses. I am an old hag from Chonburi. And my old hag advice to you: write as though you are reaching out to group of old hags, not as though you are sending a text to a friend.