We propose a static analysis method for lambda Prolog programs using a technique of abstract compilation that has already been applied to Prolog by Codish and Demoen. The method features two phases: program abstraction and goal abstraction. Since these phases require normalized programs as inputs, we present procedures for both the normalization of lambda Prolog programs and their abstraction. The analysis of lambda Prolog programs is more complex than for Prolog because the language include universal and existential quantifications, implication and X-terms (higher-order). The principal difficulty is with higher-order because a static analysis must not only discover the properties of X-terms but also how X-terms propagate them. The propagation is described by transfer functions. We apply this method to groundness analysis.