As asked above, if I were to put in a non-o application in on a Monday, would it be ready on Tuesday afternoon or Wednesday afternoon?

Thanks.

Next workday afternoon. So if Tuesday not a holiday for either country should be that afternoon.

Note that Monday is a subsistute government holiday in Thailand. Not sure if the Thai consuate will also follow substitute holidays, you might want to check their website

Edit:

Listed as holiday on their website. http://vientiane.thaiembassy.org/vientiane/en/embassy/embassy_time/?PAGEN_1=2