I agree with KC: Except the reason for the sideslip. Too complicated. Research adverse yaw, that causes the sideslip. Then read KC's second paragraph. That should complete your picture of the scenario, IMO.
Edit: Thinking some more about this and rereading KC's second paragraph I can see where it might be difficult to picture this. So when you read his paragraph pick up a piece of paper and fold it into the "V" shape KC speaks of. Now hold it up and with your pointer finger from your other hand point directly at the nose of that paper (your aircraft wing). Now bank the paper slightly while keeping your finger oriented the same, lets say a slight left bank. Your finger represents relative wind by the way. Now input a slip to this bank, from adverse yaw. The slip is fairly simple, take the wing and apply some right rudder, so the nose swings up higher. Now look at the AOA this would form on the lower (left) wing, remember a left turn, and compare it to the AOA formed on the right. Notice the difference, and thus your difference in lift.
Multipilot: Unless I am reading this wrong, "the result is a sideslip toward the lower wing" is a skid. You are referring to the nose being inward and the tail outward? The opposite of what is actually happening in an aircraft, though it is what happens in a boat. I don't know that I would use the boat scenario for this explanation. A boat skids when a turn is entered, then banks. Similar to proverse roll in an aircraft, stomp on the rudder, outside wing moves faster thus more lift, and rolls in the direction of the yaw.