Looking at the LPile website, it looks like they plot the strength of the pile in terms of a p-y curve. From the website,
Nonlinear lateral load-transfer from the foundation to the soil is modeled using p-y curves generated internally using published recommendations for various types of soils. Special procedures are programmed for computing p-y curves for layered soils and for rocks. Alternatively, the user can enter manually any other externally generated ip-y curves.
Thus, your lateral strength is based on the loading on the pile and the lateral deflection of the pile under load. I think this is analogous to a P-M curve one would generate for a concrete column.
The strength limit state then depends on your lateral soil support and the strength of the pile, so it's not really possible to say whether or not a plastic hinge forms in the pile without further information.
With a short pile length, I would agree that you're likely limited by deflection and stability since the pile doesn't have a lot of bite into the soil depth.