It's looks like a Model 51 similar to mine beside the missing lever I do notice the plate to adjust the speed is slightly different as well and the throttle lever is different too. It looks like it has the good old Briggs and Stratton on the back.
If you have a look on the engine there should be some numbers on the top cover, If it's the original engine that came with the mower you'll be able to find out what year the engine was built and it may give you an idea of what year the rest of the mower was built too.
