In order to further test the use of the sensitivity analysis approach for identifying the determinants of protein structure and for guiding the design of novel bioactive molecules, we apply sensitivity analysis techniques to study a 2-dimensional lattice model of protein folding. The 2-dimensional lattice model is simple enough so that one can calculate sensitivity coefficients, which relate the properties of a model polypeptide to the parameters that control these properties, quickly without convergence problems as in molecular dynamics simulations. The predictions from a sensitivity analysis can also be checked easily by doing many exact calculations for this model. The sensitivity analysis technique is shown to be useful for elucidating traits that might be missed without the use of this method. The study of the 2-dimensional lattice model also suggests that first-order sensitivity theory is useful for identifying residues whose modifications may have the most profound effects on the properties of a model polypeptide.