You won't know for sure until you look inside it but piston is destroyed and probably cylinder jug.

Walt Conner

That is truly a shame, and its probably the #1 reason the 2-cycle mower always had a smaller market share after the 4-cycle rotary mower entered the scene. Anybody who did that probably never bought another 2-cycle.
Who knows? The Lawn-Boy cylinder has an iron sleeve, so maybe it can be cleaned up. Some new rings and maybe you're back in business. Put some oil in the spark plug hole and see if you can get any movement now that its cooled off. I would use Marvel Mystery Oil and stand the mower up on its rear wheels so the oil can work its way past the piston - put about 2 oz. in there. Leave the spark plug out and see if you can turn the blade after a day or two soak. Don't forget to tie down the bail so the engine brake is released. You might get lucky and get it running again, but most likely you will have to replace the engine if you want to keep the mower.

I did the same thing years ago....I forgot to add oil to the gas. The mower stopped, but worked fine later on after I corrected the gas. No damage occurred to mine.