The question is not clear to me but I can say the following:
1. Lateral Load capacity of the pile (based on its material) is a function of its section modulus (S) and allowable stress. For an increase of diameter, the section modulus increases by the square. Therefore the lateral load capacity of the pile increases with increased diameter (all other things being equal).
2. The lateral soil resistance is typically based on the area of pile pushing on the soil. So, for a bigger diameter, a bigger area of pile is pushing on the soil and, consequently, a higher lateral load is resisted by the soil by larger diameters.
3. The only thing I can think of that might cause a reduced lateral load at given depth would be a function of the pile stiffness. A stiffer pile (compared to a smaller diameter pile) will deflect less at a given elevation and therefore have a smaller lateral load (relatively). This is a function of a long pile being able to redistribute more lateral loads to a deeper elevation. L-pile should give you an acceptable force resisting profile.