It's been my experience, and the experience of other coaches around the world, that runners need to be supplementing their running with a strength and conditioning program.
Over the last eleven years we have had a lot of runners come through our doors. Most were broken (from running) and had some pretty substantial mobility issues to overcome. Every single one of them were able to get stronger, improve and remediate their mobility issues, and reduce not only the miles they put in prepping for races but also drop their times significantly. The "secret sauce" - get systemically strong by including two to three intense strength-based workouts to their training programs. BTW - race preparation (miles) was kept to a minimum with impressive time reduction across the board.
So it's not a question of do you want to lift and run; it's more a question of how much do you want to lift and not run!