I'm cooking for 30 in a remote location. I do not have a salad spinner. After I wash my lettuce and tear it up for salad, I've been gently shaking it with paper towels in a covered bowl. This is helpful, but not great.
How is excess water removal accomplished in a high volume setting, like a restaurant or a cafeteria?
I can’t give you a definitive answer about commercial settings, but I do have a recommendation how to can dry your lettuce relatively quickly and if you work in batches it should be fine even for 30 guests.
A clean tea towel can be a makeshift salad spinner - place the leaves in, grab the corners and start spinning, either vertically or over your head - think spinning laundry or a lasso. You could also use a small tablecloth or any clean and largish piece of lint-free fabric. Cotton is great.
I very much recommend doing this outside because the water will be propelled outwards in the direction you are spinning (check for bystanders). Also you don’t need too much speed or spin too long, or you risk bruising the leaves. A few quick swings usually does the trick.
Shaking in paper towels might be OK as a final step, but shaking in a colander or even a large sieve is more effective at shifting large amounts of water. That actually gets rid of the water rather than just capturing it in the same container as the lettuce, and avoids having to deal with a huge mass of soggy paper which you'd otherwise have to keep changing.
You can shake more vigorously with some form of lid, such as a (light, non-breakable) plate.
If on time restraints, I recommend cutting the lettuce in half placing flat side down, give each half a quick shake and pat dry with a tea towel.
I've moved to coring, rinsing, breaking up heads of lettuce, then shaking water out by hand, placing lettuce on a clean flour sack towel, and shaking lettuce back & forth, to & fro, in the folded towel. That has worked best so far.