In Fight Club Brad Pitt weighed about 155lbs or so at roughly 6%-8% bodyfat (and he's about 5'11"). Just something to chew on while I edit this post for a proper response.
First thing's first, since it's a pretty damn good resource on fat loss and body recomposition, check out Lyle McDonald's two essays on fat loss fundamentals:
http://www.bodyrecomposition.com/fat-loss/the-fundamentals-of-fat-loss-diets-part-1.html
http://www.bodyrecomposition.com/fat-loss/the-fundamentals-of-fat-loss-diets-part-2.html
Once you've read that and let it all sunk in, use the hell out of that university gym. You're not depending on the cardio class for your fat loss, but you're taking advantage of the gym equipment they have. At least, I hope so - do they have a squat rack, barbells, dumbbells, etc? This could play a huge role in how you train. Honestly I wouldn't bother with a Bowflex or anything like that. You want to increase
strength, so the barbell program in the OP is your best bet. If that's not an option you may have to use a dumbbell program or use bodyweight resistance for strength gains.
Lateral pulldowns are a mediocre substitute for pull-ups if you can't do them yet. Otherwise they are better as a muscle-building accessory movement.
This link
might will be of better service for your pull-up and back strength endeavors.
http://www.alkavadlo.com/2010/09/learning-to-do-a-pull-up/
.