I don't think letting her loose is a good idea, at least it certainly wouldn't have been for my horse. IMO, with my horse, she is very associative. The stall is for rest, the pasture for play, and the arena for work. I watch people let their horses "free lunge" in the arena to blow off steam, and then they wonder why their horse bucks when they decide its work time on the lunge. (it also makes horrible uneven spots in our indoor, grr.) I don't want her to do anything I didn't ask for in the training ring, and she's learned that if she does, it's not really worth it, because she has to answer to me now. A horse can blow off steam in the pasture. A horse can blow off steam if you put him in a turnout where he/she normally doesn't reside. A horse cannot just tire himself out in an area where you want him to be focused on you and your agenda. I certainly wouldn't hold it against Frida if she looked at me sideways if I decided today would be a great day to train in her turnout field. I think, instead, you should begin your session with about 15-20 minutes of solid groundwork. I'm just throwing it out there, but here is what I do on an average day.
Groundwork: Walk her in hand, get her to halt, trot in hand. Get her to back up, yield her hindquarters, forehand, move her laterally. (You'll find that with all these small little requests she will be forced to pay you mind.) Desensitize her to the whip and whip cracking, get her to stand in the middle of the arena and walk a big circle around her without her moving, do carrot stretches and a series of serpentines. Just get her feet moving and keep her from being bored or distracted.
After you accomplish that and she's got her ear on you, you should be able to move to lungeing that is a bit more relaxed. Its easy to say just walk your horse, but not if she's got 100 other things to focus on and you are not one of them. He/She will just bee-line like a track horse and take off running after a build-up, and you've got to break up that straightness or else you'll be hanging on for a ride!
Do you have a subscription to HorseHero.com? I could PM you my account info. They have an amazing video for subscribers that talks about this "zone out, speed up or slow down" problem on the lunge.