Hi again, HC
If you're eating your breakfast at 7a, I would imagine that you would want to eat before you workout, otherwise you will be too hungry. Or you could have a snack around 11 and then eat after you get back. A lot of folks on LWL eat 5 or 6 small meals a day, spaced 3-4 hours apart. I did that for a while but found that it made me tend to binge more. I usually eat breakfast around 7:30a, lunch at noon, and then a snack around 3:30, with dinner at 6 or 7, and perhaps something small in the evening.
How many days a week are you planning on going to the gym? There is nothing wrong with starting with cardio, but you need to add in some kind of weight-bearing exercise at some point. If you are going every day during the week you could alternate cardio and lifting days. Or you could do 30 min lifting and 30 min cardio during your hour at the gym if you are only going some days a week.
I'm sure others will chime in with more ideas and suggestions. I guess the main thing is to find something that works for you and is sustainable.