That lockout lever prevents the recoil starter from working when the throttle is advanced too far in forward gear. The arm is pushed under the recoil pulley and jams it when the throttle is advanced too far in gear.
The engine will work just fine without the lock out lever, but a safety feature will be defeated. I wouldn’t allow other people to use the engine, they could get hurt if the engine is cranked up in gear with the throttle advanced too far.