Ok yep, I don't think it's a protecting her back issue, she just doesn't know how to use her back.
I would put an outside side rein on her for starters, and run your lunge rein through the inside ring of the bit and clip it onto a roller or girth of your saddle. If you can invest in a roller that would be ideal as she doesn't have the added weight of a saddle on her back while she's learning to pick her back up.
The outside rein needs to be firm enough to encourage her to stretch into it, if it's too loose there will be no contact other than her getting banged in the mouth every stride, so it needs to be reasonably firm but not to the point where it's pulling her head in. Without an outside in lunging, whether its a side rein, draw rein, etc. your horse is not going to benefit greatly other than maybe building up some fitness and learning to resist. He will build muscles in the wrong places and become very crooked. The purpose of lunging, particularly when trying to teach a horse how to use itself correctly, is to engage the hind legs by creating energy behind, which will travel up over the horse's back and through to the bridle. The 'front door' (outside rein) must be shut in order for the horse's back to engage and swing, if there is not outside rein the power you create behind will simply come straight out the 'front door' and you'll wind up with a horse who travels overbent to the inside and drops the shoulders to the outside. This will give you a crooked horse under saddle and you'll wind up with back and joint issues in the long run.
Now the running inside rein, if you are lunging directly onto the bit or only a cavesson, you have little influence over the inside flexion, the horse can easily drop it's shoulder and you will again wind up with a crooked horse. When the horse is more educated in its way of going, you can start lunging directly to the bit, but I always like to start my green/young horses with a running inside rein. You can control how much inside flexion you want and to a degree you have more control of the bend of the horse's body as well. You're not going to hit her in the mouth using a running inside rein either, which is going to help her confidence in taking the bit and stretching into the bridle. If she goes to take off, you can simply take that inside rein and pull her head around to her shoulder to stop her, where as with the rein connected directly to the bit she can just drop the inside shoulder and run on ;)
To put that all together, you've got a steady outside rein, an elastic, giving inside rein and a driving aid with your lunge whip, which you can use just like your legs if you were under saddle. So to drive her, use the whip behind her and stand level with her girth, if not a little behind the girth. If she's not travelling forward with those hind legs, walk a little towards her hind quarters and flick the whip at her until she goes. Now you want to engage that outside rein and ask for a little inside flexion, So as you're driving her up, you want to take a little contact on the inside rein, gently asking her to bend her poll to the inside. You may find that she'll want to resist that and stick her head in the air, so to combat this, bring her in on a slightly smaller circle around you, and point the whip towards her girth, like an inside leg, while feeling your inside rein. As soon as she gives (you'll see her inside hind leg come up underneath her and her whole body will give) allow her to move back out onto the larger circle.
Voice aids are your friends ;) Teach voice aids, she needs to know walk on, trot, canter, woah and steady. That way, you can do transitions on the lunge without having to touch her in the mouth. Do plenty of transitions, trot-canter-trot is by far the best for teaching her to use her back. But there is no point in asking for canter if she is not able to track up and give in trot first. So stacks of walk-trot-walks to get her mind thinking and making those hind legs work.
Basically your lunge work needs to reflect your riding. If you allow her to run around with her head up on the lunge, that's what's going to happen under saddle. But if you set your expectations higher, and work really hard on getting those hind legs going, the back will come soon after and as soon as she's worked that out on the lunge, if you use the same aids under saddle she will get it ;)