There is no way of knowing if a Lao girl is single just by looking at her, but there are some ways of finding out if she is single and available for a date.
Obviously one way is to ask her yourself. "Do you have a boyfriend?" If you're too embarrassed or afraid to ask her, then you could ask the question in a different way without being direct such as "So where is your boyfriend?" She will either say that she doesn't have one, or she will tell you where he is, or that she doesn't know where he is. (the last two unfortunately means that she has a boyfriend).
Another way is to ask one of her friends, family, relatives or co-workers. Someone is bound to know her marital status and their answers will usually be accurate, so ask around and you should be able to tell soon if she is available.
Check for a ring on her finger, it may not be 100 percent accurate but it's a good place to start. Try to observe the type of ring because even though a Lao girl wears a ring on her finger, it doesn't mean that she is taken. This is because some single Lao girls like to wear cheap, simple rings as a fashion trend. But if her ring looks expensive with sparkling diamond then she is definately engaged or married because these are never worn for fun.
One of these strategies will solve your queries. If you find out that she is already involved with someone then don't waste your time and move on. If she is single then it's your lucky day. You could ask her out on a date, or if you want to take things slowly then stay in touch with her. Good luck.