You would think that the dependents of the work permit holder would be allowed to enter, to keep the family together. Hopefully the OP will post here when they find out.
A Lao e-visa is a printed email confirmation. Applying online is easy although copy of passport and photo have to be uploaded. Then it takes up to 5 days to process.
I fear this may be off topic, but my British 5 year old son is flying from Bangkok to Pakse tomorrow and was going to get a Lao VOA at Pakse Airport. He will be with his Lao mother. I'm hoping they will let him in!
Without a link confirming this, it's meaningless. A few borders were closed yesterday in addition to Savannakhet International Airport - but not the land border at Savannakhet.