Meet the new boss, same as the old boss. This "idea" has been around since the turn of the 20th century.
John Browning's "Flapper Gun"
Browning designed a prototype attempting to harness the expelled gasses trailing behind a bullet. He did this by modifying a Winchester 1873 rifle. He essentially made a cup with a hole in it and placed it at the muzzle attached to a hinging mechanism with a long bar attached to the lever on the rifle. When the rifle was shot the gas would push the washer downward forcing the hinge to pull the lever forward and then spring tension brought it back and would be fired again. This was
his proof of concept gas-powered machine gun. It was later referred to as the Flapper Gun. And, to relate to modern times, someone even tried this modification, in semi-auto, on his modern 1873 for SASSs Cowboy Action Shooting and was promptly ruled illegal for competition.
There was the Francotte 1910. The Francotte is a peculiar lever action rifle that fires semi-automatically using the principle of blowback; the Martini-Henry style lever acts as the charging handle if the rifle. If so desired, the rifle's self-loading feature could be disabled, with the rifle being used like a more conventional lever-action rifle.
Francotte 1910
The there is the lever action AK-47. Pretty cool looking, but basically the lever just links to the charging handle and everything after that is all AK.
Other semi-auto bolt action conversions
Steyr M95
Steyr M1988/90
Ross MG conversion
Snabb conversion of Swedish Mannlicher
Charlton conversion of Enfield/Lee-Metford