They are one part of a number of classic theater type hardware used for joining soft flats together on stage in a way that the flats are really easy to remove for scene changes. Or for in the days before drywall screws and even double headed nails.
Basically they are put on opposing inside edges of soft flats and a rope hanging from a wise eye cleat at the top is run between the lash line cleats as if a zipper in joining the flats together. Takes but a second to remove the rope joining the scenery. Backstage handbook shows a type of slip knot used at the bottom of the flat in terminating it. Old books on stagecraft show how this type of thing was done.
Lash cleats, stop cleats, tie off cleats and or flat lash line cleats between the flats help hold the flats flush and parallel. The most difficult part short of using the lash line concept is in joining the flats initially thus the various even angle irons and various plates between flats to make the flats parallel. Than in holding up the flat and keeping it in place... wailers with keeper hooks, brace cleats, bent brace cleats, stage braces, stage jacks, or tip jacks, and stage screws at times.
Did the lash line concept before... easy to remove somewhat difficult to install and get tight enough. This especially if you can't do the stage brace/stage screw concept. Most theaters these days froun upon stage screws into the floor. Drywall screws are at times permissible but take time. Sand bags at the rear of a flat only work to an extent in keeping the scenery put at the base. For the upper part of it, while you can do a rubber bottom boom base a plywood plate that's sand bagged, it's difficult to get enough weight there quickly enough, much less remove it fast. Better yet use hinged to the scenery stage jacks that are stage weighted by extra weights for the fly system, it takes extra effort and time to remove the weights but the stage brace supports both the scenery in it's height and the bottom of the flat. This much less a good stage brace wouldn't be cheap but a stage jack would be a few dollars worth of 1x4 and plywood.
Such hardware all above is also useful for other things...
We did Noises Off last fall at my school, and our TD was trying to figure a way to roll off "escape stairs" and secure them in place when the set revolves. He tried loose pin hinges, but the stage was a bit uneven, so they'd never line up right. Same with the other two wagons of the set (no space for a turntable). Lash line cleats were the first thing I thought of--worked like a champ. Held the pieces together, straight, tight, and they didn't rely on precise lineup to slide a pin into.
Sometimes the old ways are still the better ways