Your overall fitness goals tell you if you should run after a lift. If building a lot of lean muscle is a priority, such as when training for a bodybuilding competition, you should lift heavy, skip the run altogether and refuel with a combination of protein and carbs right after to take advantage of the anabolic, or muscle-building, window. If you're simply looking to get into good shape, maintain muscle mass and increase your stamina, running after a lift will help you reach these goals. When your priority is running -- maybe you're training for a race -- running after a lift is contrary to your goals and could negatively affect your running workout. Lifting zaps your energy and may make your legs tired so you can't run with ideal form and speed.
For the average person seeking balanced fitness, a short 20- to 30-minute easy-paced run after a lift may enhance recovery. The American Council on Exercise points out that a run can increase circulation, thus providing more oxygen and nutrients to worked muscles. At the same time, a run expedites the flushing out of muscular waste accrued during your lift.