Bill,
The airbox in your photo appears to be considerably modified from what Culver originally used, at least on the LCA model. Culver used the stock airbox that the Continental A75 came with (prewar), but modified it by cutting the front of the box off from 1/4 inch forward of the mounting flange angled to the original bottom edge. This airbox had no provision for an air filter before or after the modification. However the design may separate some solids out of the intake air by directing the intake air though a 180 degree turn before drawing it upward into the carburetor. The old photos I've seen of the LFA appear to use the same or very similar airbox.
Unfortunately this style airbox seems to be very hard to come by. I have one that came with my Cadet that has been somewhat damaged, but may be usable. I've seen one on eBay in the past few years that was in excellent condition, but unfortunately I missed the auction. I've also seen a couple of others that were modified enough to not be of interest to me.