It depends because not all girls from Issan (North East Thailand) are Lao girls, but still a majority of Issan people have Lao roots, and they have relatives in Laos. Issan regions such as Surin and Buriram are populated with mostly Cambodians considering they are close to the Cambodian border.
Many Thais, Chinese, Vietnamese and other racial groups have also settled in Issan over the years so you can't just assume that your Issan girlfriend or wife is an ethnic Laotian.
Also many Issan girls were born with Lao roots but deny it considering that many Thais tend to look down on Issan people with a Lao background, or they grew up in Thailand and have adjusted to Thai society. Takkatan Chonlada is an example of a famous Lao Issan singer from Thailand who identifies herself as Thai, when in actual fact she has Lao roots.
Sometimes people know their ethnic background but they are portrayed as someone else. For instance, Russell Crowe is a world famous New Zealand born actor, who moved back and forth between New Zealand and Australia regularly during his younger years, so some people claim he is a Kiwi and there are others who believe that he is an Aussie.
At the end of the day, the race of your Issan girlfriend or wife is what she tells you. Issan is big, and is also still a relatively new region of Thailand because it used to be part of Laos so we will always have different races amongst the Issaners.