I'm in a similar position. My girlfriend is about to have our child (I'm British) and we're not married. We live in Thailand but plan to spend Songkran in her village near Pakse, with the baby. Although I'll only be there for 4 nights, I'm apprehensive about getting a knock on the door, once it becomes apparent that the child is mine.
I got fined in Pakse many years ago. I was not busted but asked by one of our staff that the police would like to see me. Went to the police station and they asked for $300. I asked for an official receipt which they were unhappy to supply, as they wanted to pocket the money for themselves,but after a bit if a stand off and an offer from me to spend time in their cells, they got the money and I got the receipt. I was married so no problem putting my name in the family book to register our daughters birth even though she was born in Thailand and had a Thai birth certificate. . Back then there were no birth certificates in Laos. I agree with timmurray in that it is nothing too much to worry about, everything is negotiable and that way not one loses face, everyone goes away happy. Keep us in the loop as to how you get on.
I agree that the law is not enforced to the point of deportation or jail time, but it is used regularly by police to raise funds through a fine. They can get you in 2 main ways - the first is that some villages within Vientiane have occasional nighttime "raids" where the police get the addresses of all houses where foreigners are known to live with Lao partners from the Nai Ban or village mayor. A group of around a dozen armed police then wake you up, let you know that you have been busted, and tell you to come to the station the next morning. You then get fined. Some Nai Ban's will leave you off the list that they provide to the police in return for gifts. The Nai Ban in one village I lived in would leave us off the address list provided to the police in return for 3 beers and a BBQ duck. The other way that they get you is if you are going through the marriage process. When you go to the foreigner control police for your "interview" as soon as they ascertain that you have a child but are not married, you get a fine. Generally this is $500 with no receipt, or if you want a receipt you pay the official fine which can be up to $5000. The $500 is negotiable also - I got them down to $150, but then the boss came in and insisted it be $500. But it is really nothing to worry about and certainly should not stop you coming to Laos. They will not stop you at immigration, and if you are not planning on getting married, you may never get caught. The very worst thing that can happen is losing $500, which stings for a few days, but isn't the end of the world.