Now all Thai embassies/consulates are on eVisa system. No appointment any more. You must apply for a new visa on eVisa system by choosing the embassy/consulate you want to apply to.
You will go to the embassy/consulate in Laos to pay the fee without an appointment, once you complete your application (except for the fee payment) online.
You can start uploading documents in advance to prepare. But you cannot complete your application until you upload the entry stamp to Laos.
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