To quote Ramsey Dewey:
So the best movement that you can do for
cardio in Jiu Jitsu is Jiu Jitsu. Do more
rolling, for example, do more drills and
by drills I don't just mean going
through the motions. I mean, you know, a
actual resistance with a specific
objective and the same thing with Muay
Thai. One of the best cardio drills from
Muay Thai or muscle adaptation drills is
heavy bag work. Make sure you're getting
your rounds on the bag every single day.
Three rounds on the bag is a good
benchmark. if you're not doing that then
He talks a bit more at length about having previously done running, but having to quit in part due to his joints, and in part because he found that it just wasn't translating to more endurance during a fight.
In your case, you don't have a heavy bag over your lunch time, most likely, but you probably can shadowbox. He goes on more at length about the value of shadowboxing in some of his other videos, but a quick summary is that it's valuable, because you're training the same moves that you're going to be doing in the fight, but you need to train with intensity, and mindfulness. Don't just run through drills, but rather do the drills as if you're actually striking the target or dodging the blow, at speed and with power.
I haven't had a chance to track down one of his talks specifically on shadowboxing (this one works by title, but is largely about improving one's fighting through observation and shadowboxing), but from his entry on junk training:
Shadowboxing without visualization is junk training. Shadowboxing with proper visualization is game changing good stuff. In fact, shadowboxing is so important that Jack Dempsey considered it second only to actual sparring in terms of importance for fighters. But how often do you see people shadow boxing at that level, as opposed to simply working up a sweat before doing their bag work?
If 30 minutes shadowboxing doesn't wear you out, but 15 minutes of fighting does, well, that tells you something about relative effort. Some factors are very difficult to reproduce, like the lack of predictability that you'd get with an actual opponent forcing you to reverse directions in mid-swing, or the force of impact, but just consciously throwing the techniques at full force (obviously, you have to pull those punches in the end to avoid damaging your body, but in an actual fight, you'd be doing the same thing for missed blows), and building in "sprint" movements where you don't just duck, but actually drop as fast as you can, as you would under a real strike, will help you to bring realistic tension and strain into the shadowboxing. And, of course, make it dynamic. Don't just go through a strike combination over and over again, but start to interrupt it with a dodge from an imagined incoming attack (again, doing it with purpose, as if someone actually were striking at you) before resuming.