There are definitely lever action shotguns, but I doubt there are many SBS versions. I don't think I've ever seen an over-under SBS either. Maybe someone will post one up. Pump, side-by-side and single shot break actions are probably the most popular types to make into a short-barreled shotgun.
Here's mine. This is an H&R/NEF Pardner Pump 12 gauge with a 12" barrel. The story on this gun is that I needed a "test case" for the ATF's new eForms system so that I could explain to my clients how to use it. I already had some SBRs, but no SBS. I didn't want to spend a lot of money building a gun to "test" the system, so I went with the cheap shotgun. It's a clone of the Remington 870, and most parts interchange except barrels. This shotgun can be bought for under $200. It started life with a 18.5" barrel because it was the home defense version. I paid $200 for the tax stamp, and it was approved right at the 3 month mark. The furniture is Magpul's SGA stock and foreend for the 870. Fits perfectly on the H&R/NEF. I like dying Magpul stuff, so this is all a dark blue (RIT dye combined with FDE furniture). The hook on the front is Magpul's hand stop. It hangs too low because there has to be a rail section to attach it to. Not pretty, but it works and is nice on a short barreled shotgun. I cut the barrel down to 12 inches, reblued it and put a new bead on it. I had to grind the underbarrel lug for the magazine tube off the part of the barrel that was removed and weld it back on the barrel. I also had to cut down the magazine tube. Rather than re-thread the tube, I cut the tube behind the cap threads, shortened it, and then welded the threaded section back on. The tube got reblued as well. The magazine spring didn't need to be shortened. It holds 4 shells in the tube now.
With the cost of the shotgun, tax stamp and Magpul furniture, I have probably $500 into this gun. It's a very light and handy gun. Points nicely, held in one hand, it hangs by your side nicely, and with reduced power buckshot loads for home defense, it's not too rough. I'm very glad I built it.
Aaron