Do I need my old job to cancel my visa before applying for a new Non-B visa in Laos?

You won't need the cancellation stamp to GET the visa via the online system in Lao, or enter thailand, BUT you will have to have that extension cancelled or you won't be able to get a new extension on this Non-B you're comin' back into the country on until you do <- and if you don't do it before you go you will be fined when you do go to cancel it

𝘀𝗵𝗼𝘂𝗹𝗱 𝗺𝘆 𝗼𝗹𝗱 𝘄𝗼𝗿𝗸 𝗰𝗮𝗻𝗰𝗲𝗹 𝘁𝗵𝗲 𝘃𝗶𝘀𝗮 𝗯𝗲𝗳𝗼𝗿𝗲 𝗜 𝘁𝗿𝗮𝘃𝗲𝗹?

I would say YOU need to go get the extension cancelled from the immigration office that issued it, then leave the country and go apply for the new Non-B visa in Lao