Cardio burns more calories during the exercise, but weight-lifting builds more muscle which in turn raises your RMR (Resting Metabolic Rate). I have a little over an hour to workout each day during lunch. Should I spend my time lifting, running, or a mixture of both? (if I should be doing a mixture, what should that mixture look like? e.g.(10-20% cardio))
Lifting everyday wouldn't give your body enough time to rest so you'll have time for some cardio no matter what.
My previous trainers have all recommended lifting for 30 minutes three or four days a week and cardio the rest of the time. I've had pretty good results following that.
Strength training and cardio provide a potent mixture to burn fat. The problem with strength training alone is that it burns fewer calories than you would during cardio. For example, an hour of intense strength training will burn between 270 calories and 450 calories while you exercise (depending on how heavy the weight is). Running at 6 mph for an hour will burn closer to 1000 calories (depending on how heavy you are). The other difference is that as your body builds more muscle, you are burning more calories all the time.
If you do a strength training program like Rippetoe's Starting Strength or Medhi's StrongLifts 5x5 you are working out 3 days per week. Each workout is up to an hour long depending on how much rest you need between sets. You will lose fat, but maybe not as quickly as if you incorporate cardio. NOTE: you do get a cardio workout lifting weights.
In my situation:
I started the StrongLifts 5x5 program 6 weeks ago and worked up from just the bar to the following weights:
Each session you go up by 5lb (except deadlift where you increase by 10lb). I will say that it is quite challenging. Just from doing the weight training, I have to eat more just to get through the next session. In the mean time my neck, arms, chest, hips and thighs are getting bigger while my gut is getting smaller and the scale stays the same (+/- 5lb).
I do top off the weight lifting with 20 minutes of cardio. I'm currently running 1 minute intervals on the treadmill. The combination puts me at 90 minutes each time I'm at the gym. I'm maintaining weight, but losing my gut which is what I really want anyway. I've found that my cardio work is much easier due to the lifting I've done.
In your situation:
I would recommend doing strength training Mon, Wed, Fri. In your off days (Tue, Thur) do cardio for 20 minutes of work and 5 minutes of cooldown. Start with a light jog/run interval of 1 minute each. If you have 2mph difference between the two intervals you'll be able to recover for the next run interval. Increase by 0.1 mph each time you do you cardio until you just can't get any faster. This limit should be more of how your legs are trying to keep up than your heart/lungs trying to keep up.
Your initial workouts will be light enough that you won't have any problems. When the weights get tougher (probably around week 6 if you are like me), you might have to back off on the cardio. Your gut will continue to get smaller as you get stronger.
Strength training burns more calories per minute of activity than cardio, it's scientifically proven. It's true, you shouldn't be strength training every day of the week because your muscles are worked so hard they need to rest and repair. But you also shouldn't be doing intense cardio every day. A combination of both is ideal, but if for whatever reason you couldn't do both, you should weight lift because it's more effective at burning calories, while also keeping your muscles. If you just did cardio, a third of the weight you lost would be muscle mass, your body would weigh less, but look worse.
Cardio is much more important than weights for losing weight.
In summary: while you can raise your RMR by building muscle, it is an extremely slow process when compared to the speed at which you lose weight through cardio. They found that weight-lifting is a minor factor in weight loss; the determinant factors are proper nutrition, cardio exercise, with some influence from typical health considerations (proper sleep, mental health, etc).
So for your case, if your goal is to lose weight, spend the whole time on cardio.