Should I really staying at a walking pace?
Yes. The most important thing when you start proper endurance training is to improve your aerobic metabolism—i.e. build a base. For most, the initial pace will be very slow and not very stressful. That will change over time.
Or should I be mixing in running?
Only in two instances: if you can run under your aerobic (not anaerobic) threshold; or if you need a few weeks to sharpen for a race.
Also, I see a lot of focus on the HR training but not a lot on lifting. Do people run and lift on same days or alternate?
Search this site for strength training or check out one of our books. Lifting is an important part of any endurance program, so long as it’s done where it counts and without a focus on creating dead weight (i.e. mass.)