I would not presume to tell you what you could and could not do after a lumbar fusion. Best to talk to the operating surgeon, and you can also ask for a referral to a physical therapist for more information about activity levels.
I've heard you have to be about 1 year post surgery before beginning any exercise programs? A friend of mine had a cervical fusion and she was told no heavy weightlifting, which is really a drag, because she loved doing those kinds of workouts. But she deals with it. Also, high-impact might not be in the equation, but again you need to check with your doc and not rely on a bunch of Internet yahoos for this kind of advice. Did you have a cage inserted?
Anything mild is probably going to speed healing as soon as you feel like you can do it, like walking or swimming. If you get a negative on the running or high impact, the next best thing to reach that level of endurance would probably be a ski machine in the summer, like a Nordic track set-up, and cross country skiing in the winter if you live in the snow. Frankly, it's probably better for you than running anyway.
But I'd check with the doc. I'm a long distance runner myself, and I know that being away from it would drive me crazy!
Keep us posted on what you learn about this. Really, check with the doc first. I presume you already did some research on the tubes about this - medical websites, orthopedic websites. You can also post on the orthopedic forum here, I'll bet there are post fusion patients over there giving advice.