Aerobic training and Weight Lifting

Is it possible to get strong and put on lean muscle while lifting weights and doing aerobic training?

I like to run but am looking to build up some strength and some muscle should I stop running?

I feel as though running is natural and good for the body . can the two not work together?

It is possible, especially if you're built like a pole. But at some point, jogging will take away from your muscle gains.

Define "natural". If we are talking about whether or not nature intended human beings to jog, the answer is probably not. Primal humans probably did sprints (away from someone/something dangerous) but other than that, cardio was walking. Not to discourage you from jogging though. Cardio is very important.