The vertical component of the lift must equal the weight (which always acts downwards). It really helps to draw a simplified diagram.
The angle theta must be equal to the angle between L and the vertical because when the lift is acting at 90 degrees to the horizontal, the wing is flat (ie, theta is 0). When the plane rolls rolls to one side, the angle between the horizontal and wings increases from 0. Therefore, the angle between L and the vertical must also increase and this angle is equal to theta.
You should now be able to construct a right angled triangle with theta and L.