Just start your Non-O application now, you can look through the required documents there.
Input what you can, and just save it and continue when you've got the documentation required.
Submit when you have proof that you are in fact in Laos.
In Vientiane you have to go to the Embassy to pay in person.
I did this a couple of weeks ago. Non-O based on Thai husband.
if you are applying because of Thai spouse, submit a signed and dated copy of your spouses ID card and have your spouse date and sign your marriage certificate.