@Michael *******************
Yes, but make sure you're aware that Monday and Tuesday are Thai holidays. So you'll need to be fast.
You can pre-fill most of the application on the e-visa website. Then as soon as you enter Laos (I would go Tuesday) upload your entry stamp in your passport and submit your application. Then first thing Wednesday morning (I'm talking EARLY, because they will have been closed for 4 days, there will be a lot of people there), go get in line at the embassy to make the payment for your application. They accept payments from 9-11 AM.
Then you'll just have to wait.