Why are you training twice a day? Is leaning out your primary goal or a secondary one?

If leaning out is the primary goal, reduce the intensity of your aerobic sessions to be simple fast walking for 15-30 minutes fasted in the AM. If you IF you'll not need anything to recover from this. If you don't, eat a small low carb breakfast after (like a few eggs.). Keep your strength sessions heavy and hard, and eat the majority of your calories and carbs after that workout.

If you are required to do both sessions then take BCAAs before both workouts and only eat post workout. Take coffee with your carbs after your morning sessions as it improves muscle glycogen uptake. Still keep the majority of your carbs and calories after the strength session.

To lean out you'll need to eat less food, so that is why I'm not recommending two-a-days. Fewer calories mean less recovery time and it will be a struggle (for most people) to keep it up for the time it takes to drop bodyfat.

I don't actually know.

However, from what I've read (particularly on Leangains), I feel that the best route is to work out on an empty stomach and eat a pile of carbs/protein afterwards.

And yeah, fasted workouts do seem to work for leaning out .

If your goal is to lean out a little, I personally favor them post workout. First, you'll allow yourself more opportunity to burn some of your own reserves during exercise if you restrict both carbs and fat until your post workout meals. Second, you'll have improved insulin sensitivity post workout, ensuring that those precious carbs get used properly. Third, exercise can be really efficient at acutely increasing cortisol, so I assume that consuming some carbs post workout might mitigate that response a little.

However, if you're competing at a high level, it might be a good idea to drink some diluted pedialite (glucose) during your workout, or eating a banana or some starch before hand.

I favor fasted workouts followed by whatever PWO nutrition gets you set for the next planned workout or athletic practice.

In super short summary, I believe that this best simulates a successful hunting trip, and reinforces both the exercise and the apportionment of PWO nutrition to the most advantageous parts of the body.