Forget about the ETA as it's been postponed indefinitely...wait for official Thailand government information and ignore old information on the internet....
Make sure you check your visa requirements for Vietnam BEFORE you travel
Your passport must have at least 6 months left before it expires at the time of entry..
It's unlikely the airline will allow your friend to board the flight on that old passport.
You don't mention your friends passport country?
But some countries allow express passport processing for an additional fee..
And if they have a passport from a country that requires a visa BEFORE you fly then that also could be a problem arranging a last minute visa with limited time..
If they have a visa already on the old passport number that will not be valid anymore
It's at the discretion of the Immigration officer you are dealing with on the day you enter..
If in the opinion of the Immigration officer your travel history looks more like someone trying to remain in Thailand long term using visa exemption then you could have a problem..
Personally I would fly in Bangkok from Loas as that's likely to a more reliable way to enter but who knows..
Good luck .
You may want to consider a visa application in the future BEFORE you travel
Should not be a problem based on your plans and you will get another 60 day visa excemption entry when you return to Thailand..
However Keep in mind if you repeatedly enter Thailand consecutively on Visa excemptions then you stop looking like a genuine tourist and start to look like someone trying to live in Thailand on Visa Excemption entry and that could eventually become a problem..