To prevent both lower back pain AND any knee or leg pain that could be caused by running, the first (and most important) preventative measure is to strength train. Lifting weights or cross training in such a way that builds up those muscles, strengthens them, and helps them to carry and bear weight easier will help them not only hurt less while you run, but help them to safely endure the high impact that is often associated with running, and which often causes prolonged back or knee pain problems. Focus on muscle strengthening workouts that target your core, hips, and hamstrings. (For some inspiration, planks, squats, lunges, and deadlifts are excellent options when you are in the gym.)
Along with strength training, always be sure to stretch properly before each and every run. Dynamic stretching is your best bet in this scenario for helping keep the pain away. Running on "cold" muscles (i.e. muscles that have not been warmed up) is one of the most common way runners end up dangerously pulling something and injuring themselves. In fact, cold and tight muscles are so much of an issue for runners, and can subsequently cause such major problems, that most professionals and coaches strongly advise others to stretch and foam roll at least twice a day. This way, your muscles will be less likely to stiffen up (and stretching regularly means it becomes less difficult to stretch them because the muscle memory has become used to the pressure). Massage is another excellent way to keep muscles loose. It can be an expensive habit, so you probably can't get a massage multiple times a week, but a few times a month can help do the trick. It also does not hurt to take an over the counter muscle relaxant and pain killer, like ibuprofen, before heading out for your run.
Finally, what you wear DURING your run can make all the difference in the world - at least when it comes to your shoes. Make sure you invest in a decent pair of running shoes that provide plenty of structure and support, so that some of the shock of repeated pounding can be absorbed into the shoe and not rebounded back into your joints.