If lift = "1" and weight = "2" wouldn't the load factor be 0.5 not "2"? ie lift is less than weight so the aircraft would be be feeling 0.5G?
In a stable turn, the weight (say "1" unit) is obviously constant however the lift is now pulling at an angle to it.
The angled lift is being used to cause the aircraft to turn. If we maintain the same "1" level flight unit of total lift, angling it sideways means lift no longer balances the weight force.
To balance weight in a banked turn, we will need to increase the total lift from the wing so the component acting directly away from the earth (and so neutralising weight) equals "1" unit.
The wing may therefore need to be be producing say "2" units of total lift (depending how steeply we bank the aircraft) - part of this extra is acting to exactly neutralise weight, the rest is causing the aircraft to turn by accelerating the aircraft constantly towards the centre of the turn.
The only way you could get a 1G turn would be to turn without banking (skid it with rudder?) or somehow otherwise get some other force than lift to neutralise your weight
You in the cockpit feel the "2" unit lift force as an acceleration and you feel pushed into the seat with twice your normal weight.