You need an air fuel ratio of around 13:1 for the mower to run.
The needles & jets control the fuel side the choke controls the air side.
So if you need less air then either you do not have enough fuel ( dirty carb, blocked filter etc etc ) or after the fuel has been mixed with the air , more air is getting in leaking butterfly (carb, leaking manifold, gasket etc etc )
Water tends to build up in the bottom of the carb so while most of the fuel is being drawn from the lile circuit it will run but as you start sucking fuel from the bottom you get water being sucked into the carb and unfortunately they don't run well on water.