What is the reason you are lunging so much?
In my opinion, lunging fifteen minutes, four to five times a week ("before every ride") is a lot, especially for a young, "out-of-shape" horse already going to get ridden. Lunging to get the horse's attention on you is one thing, but to simply tire them out (before you ride) or exercise (as opposed to riding them) isn't a good habit; in my opinion, if you need
to lunge before every ride, then something in the equation is wrong. Lunging is physically strenuous (small, tight, constant circles) and mentally boring ((in their mind) aimless circles) for a horse; do not over-lunge. When conditioning a horse, especially a young, out-of-shape one, you want to start gradually and then try to make it a little challenging, yet not overly strenuous. You also want to try to make it fun so they don't dread their "job."
made a good suggestions ground poles, cavalettis, and hills. I think what you are doing is a good start - having her ridden about four to five times a week, about an hour each. I like (and so do some horses) to work on trotting on a (relatively) loose rein for fitness.
I know she is still green so for now, I'd work more on other things, such as obedience, reliability, balance, relaxation, and various other skills. The more you work with her, the more in-shape she'll get. (Duh! What I'm saying is to work on other things and have other goals besides soley focusing on her fitness.)
I know everyone has a different opinion on work load for young (and/or out-of-shape) horses, but make sure you aren't asking too much too soon.
The saying "it takes as long as it takes" can and does apply to horses and their fitness. There is no set schedule that the horse will be [this fit] by [this time] if you do [this work-out]. Every horse, like people, are individuals and their body handles exercise and conditioning differently. Some see a difference in a few weeks; some see a difference in a few months. Just think, every time you go out and work her, fitness wise, she gets just a little bit better.