>you can't lift weights and gain muscle (i.e. grow) without also gaining fat
Of course you can. I'd be happy to share my Google sheet of daily weight, losing about 0.06lb/day, and my BodPod measurements showing going from 28% to 20% body fat while gaining 2.5lbs of muscle mass. Sarcopenia would have taken another 0.5lbs of muscle in that one year period.
Drew Baye has several articles on losing fat while gaining muscle. In the first few pages of Body by Science, Doug McGuff defines health as (1) the absence of disease and (2) a balance between anabolic and catabolic processes. Except McGuff makes it clear that almost the entire population in the developed world lives in a catabolic energy state, eating way more than we need, never flushing the stored glucose out of our muscles, the tank is always full. But while that is happening, sarcopenia [catabolic] is removing muscle mass as we age.
Health: A physiological state in which there is an absence of disease or pathology and that maintains the necessary biologic balance between the catabolic and anabolic states.
Fitness: The bodily state of being physiologically capable of handling challenges that exist above a resting threshold of activity.
Exercise: A specific activity that stimulates a positive physiological adaptation that serves to enhance fitness and health and does not undermine the latter in the process of enhancing the former.
Free PDF of Nautilus Training Principles: Bulletins No. 1-3
Summary of research and evidence-based exercise as of 2009:
Body by Science
Author Doug McGuff MD has been operating a training facility since 1998, 100-120 client sessions a week, and he reports zero injuries to date. Most injuries come from excess force/acceleration, so pick an exercise protocol with very low acceleration that seriously fatigues the target muscle.
 - http://www.amazon.com/Body-Science-Research-Strength-Trainin...
Body by Science — Doug McGuff, MD and John Little 
This is, by far, the most interesting and useful resource I have found when it comes to fitness:
The author covers cellular biology and debunks ideas such as "cardio workouts", treadmill bunnies, jogging and walking around your neighborhood to loose weight with plain-old science. Here you'll learn about the cellular metabolic process, Krebs cycle, Insulin resistance, fatty acid synthesis, glycolitic cycle, Cori cycle, Bohr effect, glycogenolysis, amplification cascade and whole host of other topics that are important, relevant and reasonably well understood.
What's more important is that everything that is proposed in this book is backed by science and scientific studies. It's like open-source software. If you care to dive deeper into why something works the way it does the scientific references are provided. The book has over 25 pages of listed references (about 10% of the book is reference data).
Anyhow, one of the claims of the book is "12 minutes a week" every seven to ten days. In other words, that's the actual time under load you need every seven to ten days to affect significant changes in your body. This does not include time walking around, watching TV or resting. Time under load.
I have to say that it works pretty much exactly as advertised. After reading the book I tried it and had a friend try it. We'd spend about fifteen minutes under load at the gym once a week. For me it changed to fifteen minutes every 9 to 12 days (you track your data in order to determine frequency). I got stronger with every passing week. Something that I was not able to do without a ton more effort in the past.
If you are interested in learning about this, start with Dr McGuff's (the author) videos:
My advice: cut simple carbohydrates out of your diet completely (veggies and animal protein only) and start exercising as much as your fatigue allows you. Read this book too: http://www.amazon.com/Body-Science-Research-Program-Results/...
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