My DS is a runner too and struggles to keep weight on. Many runners are too skinny to even be good runners, frankly. The super-skinny guys are marathoners, for 1-3 mile races you need more muscle. While lifting may make the muscles you have stronger, it won't add muscle. You need calories and LOTS of them.
I think most high school runners don't eat enough. The base calorie intake for a kid your age is probably around 2,300 calories a day and then add workouts which add another 1,500 calories a day -- you need close to 4,000 calories a day just to maintain your weight -- you want to add weight -- you need to be near 5,000 calories a day.
Get eating!