Hi and welcome to the forum. Vientiane is not a major airport and so you will not get direct flights there from anywhere outside SE Asia. The air hub for South East Asia is Bangkok, and you should be able to get a direct flight from LAX-BKK - shop around for prices, though, as they might vary drastically.
When I travelled in Laos 6 years ago Lao Airlines had a very poor reputation for safety. Things may have changed since then, but it's worth looking into their reliability. From the schedules they currently seem to fly four times a day from BKK-Vientiane, as do Thai Airways, who have a much better reputation.
As an alternative, have you considered a sleeper birth on the night train from Bangkok to Vientiane instead? Fly to Bangkok, spend a day or so there, get your visa for Laos at the embassy there, and then get a train ticket for the night train... waking up in Vientiane mid-morning. You won't really be losing precious time on your holiday as you're travelling overnight. It's a great experience too and less than $25 for the journey one way.
Join us over on the
Thailand Forum and we can give you plenty of advice about Bangkok!
Safe travels,
Steve