Jenn,
I have used walking strong in combination with heavyish lifting.
I use lighter weights than I would use to do the upper body work in walking strong - just for safety, because I am walking while doing the weight work. I cant focus as much on form as I would need to with heavy enough weight because I am on a treadmill.
I consider walking strong cardio. When you walk carrying weights, rather than strength training, what you get is an added challenge for your heart because your body has suddenly become that much heavier.
I consider the muscle conditioning effect from doing the upper body exercises a small bonus rather than "a full" upper body workout.
Sorry for being long winded. I say - yes, you can use walking strong with heavy lifting as long as you are using light dumbbells (5 pounds is what I use). If you have DOMS is a muscle group simply walk holding the weights during that exercise. For instance, if you hit biceps hard the previous day and have DOMS, when the biceps track in walking strong comes up, just walk that section holding dumbbells.