Does she fall back to a trot evenly throughout the arena or is it in a specific spot?
How do you ask for each gait? I find that people with lazy horses tend to share a common rider error. Often, the rider anticipates that their horse will be lazy and uses quite a strong cue to ask their horse to go forward. This never teaches a horse to be softer because there is never a soft cue to start with. On the other hand, I see riders with any horses do the opposite. If a rider is worried about a protest they tend to nag and just keep asking their horse to move forward very softly. The same problem exists here, since you never increase the pressure to make that soft pressure the good deal, the horse remains dull to the leg.
Can you use a dressage whip on her without her protesting?
The first thing I would address before you worry about anything else is getting this mare more forward. Don't worry about particular gaits, just getting her in front of your leg.
You can not expect her to maintain good forward motion, if she is not forward in the first place.
I would start at the halt. Ask her to walk forward with a very soft squeeze of your calves. Do NOT allow a sluggish step forward where he just drags herself forward on the forehard to be acceptable. If she moves sluggishly (or not at all), then increase the pressure. Take your dressage whip and thump her behind your leg or on the hindquarters, then bump her more firmly, whack her, whack harder etc until she moves forward. If you can't use a whip on her, kick, go from a soft squeeze to bump with your calves, to kick, kick harder etc. It does not matter what gait she ends up in, a trot, or lope. You are applying pressure until you feel like she's not lollygagging and moving sluggishly. Even if you are applying pressure pretty firmly and she's loping, if you feel like you are pedaling a bike and as soon as you quit pedaling, she will quit, she's not forward enough for you to quit applying pressure. As soon as she feels like she's in front of your leg, leave her alone completely and let her continue forward for a few strides. Do NOT keep your leg on, you want moving forward to be the good deal here. Then bring her back to a halt and begin again.
You'll see improvement pretty darn quickly. After a few repetitions you'll notice that she is taking a larger, more forward stride. She'll also begin to stay forward for longer before she starts to die down and get behind your leg, don't worry about that just yet.
When you have a nice forward walk to start with off a squeeze, then you can teach her to maintain it. Ask her to walk on then allow her to get behind your leg and then stop. As soon as she stops, correct her. Skip the squeeze and immediately go to your dressage whip or begin with a light kick. You have already asked her to walk forward nicely, this is the correction so it will be more firm. As soon as she's in front of your leg at whatever gait, leave her alone.
This will teach her to be responsible for herself, she should maintain the same amount of forward until you ask for something else. Since you are leaving her alone when she goes, it's the easy thing to do. By allowing her to make the mistake of stopping, you are letting her learn that is the more difficult choice to make.
When she can maintain a nice walk, ask for the trot from the walk. Already you will see a heap of improvement. When you've repeated this at the trot, ask for the lope. Each step that you work on will improve the next. When you get to the lope in a couple of rides, you will find her to be much more forward.