Did you go to the thai consulate in Vientiane website and read the eVisa application steps?
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You go to Lao, you log into the eVisa online website, make a profile, select your country of passport and then that you're in Lao, then you select the Vientiane consulate. Then you select Non-Imm visa and the correct choice on the drop down for the B visa you want
Then you fill in the data, upload proof you're in Lao (visa/entry stamp) the required documents in the required places, check that there are no errors and submit your application.
You'll get a confirmation to PRINT out and you take that to the consulate to pay for the visa (2000baht)
After that you just monitor the status of your application in the eVisa system. When it's approved they'll send you an email with the visa in a PDF file which you print and give with your passport to the officer when you stamp back in to thailand.
Keep in mind today is the last day the consulate is open until next Monday (the 14th) 😮 because tomorrow and friday are holidays, so you're gonna camp out in Lao for 5 or 6 days if you just got there now to apply online 🙂
They post they have a 10-15 day processing time but really it's just a couple business days after you pay