Foreigners without Lao citizenship are not allowed to have ownership or co-ownership of property in Laos by law, regardless of whether you have migrated to Laos or not.
Be aware that if you buy a house with your Lao wife, the property will be in her name irrespective if you are married under Lao or foreign law. If she leaves you, she can and probably will get the house along with all the money you put into it.
If it's going to kill you to put property in your wife's name, then one option for you is that you could put it in the name of a relative in Laos who you can trust. But having said that, not many westerners will have relatives in Laos unlike the Laotians living in a foreign country.
Sometimes this can cause conflict because your Lao wife may be unhappy about the property being registered under someone elses name. It shows her that you're married to her, but you don't trust her.
Living in a rented house or apartment together is another alternative, but your Lao wife will eventually like to buy a house especially when she has kids.
You could enter an agreement with your Lao wife for the house to be divided in the case of a divorce, provided that relatives and a village headman are also aware of the agreement. This doesn't protect you one hundred percent but it's something.