I know the key behind weight lifting and strength training is giving your body time to rest, recover, and build muscle. So you can't go back to gym or even biking the day after.
What about the day before? Can I do heavy aerobic exercise on Monday and lift weights on Tuesday?
If you're focusing on strength and mass gain, you do best by prioritizing strength and mass gain.
Doing other things (cardio, biking, hiking) might be consistent with your goals, if your goals are not primarily strength and mass. But our bodies have a limited capacity for physical recovery. You have to decide how you want to allocate that resource.
Speaking to the specific scenario you pose, a weekly schedule with heavy aerobic exercise on Monday and lifting on Tuesday would mean that the body would be devoting recovery resources on Tuesday to getting better at aerobic exercise, which would detract from the mass and strength gains that could be had by resting on Monday instead. You will be weaker on Tuesday due to Monday's work, though as a novice, this weakness could be imperceptible or negligible.
I find that putting metabolic conditioning at the end of a lifting workout, or the day after, allows for better recovery alongside a strength program. I intend to see what Tom Kurz has to say on this aspect of programming, but have not gotten around to reading his Science of Sports Training.
What you're describing is the reason many people work different muscle groups on different days. In short, yes, you can.
Let's say your aerobic activity worked your legs primarily, stationary bike for example. The next day may be a great day to do arms. However, you may want to gives your legs some rest.
Aerobic activity is building a different type of muscle than anaerobic activity, refer to: http://sportsmedicine.about.com/od/anatomyandphysiology/a/MuscleFiberType.htm
Let's keep in mind that you should be exercising every day, but that doesn't necessarily mean a grueling workout. If your primary concern is your heart (which it probably should be and is!), then make sure to never overlook cardio. Lifting weights, on the other hand, can help to boost your metabolism and offers benefits of its own: posture, strength, endurance, etc.
If you keep yourself to just one set of reps for each exercise at high intensity, it's fine even the day after. I do 1-2 strength workouts per week, and I cycle everywhere I go, including the day after lifting. It works fine. Now it's possible that that adds an extra day or two to my recovery, compared to what I might do if I didn't cycle at all, but that's not really a problem in my book. I'm still making significant strength gains at each workout. Doing aerobics the day before definitely isn't a problem.
If you're planning on doing Aerobics - Lifting - Rest - Aerobics - Lifting - Rest you might run into a problem with strength gains due to effectively only having 2 rest days, and only one of them is a real rest day, but if you do Aerobics - Aerobics - Rest - Aerobics - Lifting - Rest - Aerobics - Aerobics you shouldn't have any trouble making continued strength gains.
