New runner - legs not lungs are the issue

I'm a reasonable athlete (soccer, biking) but have never been a good, consistent distance runner. I'm now doing Couch to 5K, just finished week 2. I find while I'm running that I'm not out of breath so much as my legs get tired (lactic acid?). Has anyone else had this experience? Do I just need to build up my vascular fitness?

Yes, building up the cardio when you start running can happen in a fairly short amount of time. Building vascular components takes a bit longer, and finally building up the muscle/skeletal/tendon/ligament component takes even longer. This is why you will consistently hear the advice to take your time and build slowly. It is all too common to see someone starting out do to much to soon and end up injured because the adaptations that take longer are not up to the ones that have already happened.

If your legs feel like they are burning however, this is generally because you are at your lactic threshold, which means you are running too fast for your current state of developement. Although there are certain running workouts that are intended to be at this point, they are not in c25k. Warm up a little, take a short break and then start your workout. Run slower so you don't feel your legs burning and you will progress faster. As you run more your endurance and speed will increase naturally.