Does Laos have a large vegetarian population?!

First, Thailand and Cambodia do not have large vegetarian populations as their definition of what is "vegetarian" is very different from what Westerners refer to as "vegetarian". That's why even Thai and Cambodian "vegetarian dishes" have either fish sauce, shrimp paste or even both.
Laos is a poorer country so many people have a vegetarian diet for periods of time but would otherwise eat meat if given the chance.

If you are going to any or all of those countries, make sure you specify "no fish sauce, oyster sauce, or shrimp paste please" when you order. Many restos are familiar with Westerners' habits and "likes" so that should not cause too much of a problem.

I have business partners from Cambodia and Thailand and been to both countries many many times. We are currently negotiating with an exporter (and the government) to bring in the famous award winning Laotian beer, BeerLao

yes

uhhh, yeh, have you been to Thailand and Cambodia?
They're nations of Buddhists, OK, but there are a lot of meat eating folks too, even the Buddhists.
Laos is just as Buddhist as those places, and you get rice, sticky fish, herbs and spices, noodle soups, beef, chicken, tofu and vegetables made in almost the same manners.

A popular dish is Larb- marinated fish or beef. They have papaya salad, just like Thailand, sticky ruce and peanut soysauce marinades.
They do a lot of barbeque foods on a stick-fish, tofu, gluten and meat on sticks, on street vendor carts.

They do lots of pad sen, and pad yao- noodles, in soup and plain noodles with spices- you can get vegetables of the beef version.
Lemon grass and galangal and chili is popular- those flavours are everywhere.
The French left a good culture of good coffee and baguettes with apricot jam, in the mornings.

The Lao's are the same vegetarian as Thai imo.

Travelled a lot there.