Yeah HL2 first, Lost Coast was originally part of the Highway 17 chapter of the game, but it was realeased to show off HDR and stuff I think. And there's nothing important to the plot in it.
There's another topic on this somewhere but I can't remember where I read it, and I'm too lazy to do a search. Anyway, Half-Life2: Lost Coast is just a small playable tech demo to show off HDR. It has no relevance to the Half-Life story.
So it doesn't really matter in what order you play them, but you'll have a better time if you play Half-Life2 first! simply because its actually a game and not just a tech demo.
Which will spoil weapons and enemies for you. You may not even figure out the function of one or two weapons given that HL2 is the one that takes the time to teach them to you.
Completion time for Lost Coast is around 10 minutes or so. You're there to look at the pretty graphics, not to play the game.