There is no lateral force on the wheels.when cornering. The bike is leaning into the corner, that converts any lateral force into perfectly straight down force as far as the bike is concerned. You would only have lateral force if the bike is unable to lean, such as in trikes.
You are incorrect. The lateral force is the centripetal force that pulls the bike around the corner. When riding in a straight line, the normal force is perpendicular to the wheel. Pedaling
does introduce some lateral force to the wheel but we’ll ignore it for now.
In a corner, the downward force (red arrow) is at an angle to the normal force. The forces are a combination of the normal downward force due to gravity (green arrow, which is in the wrong direction, sorry) and the horizontal force on the wheel due to the centripetal force on the wheel that pulls the wheel around the corner. For the wheel’s point of view, the rim is bent out of line with the hub.
