The paper presents the numerical solution of a projected generalized continuous-time algebraic Lyapunov equation (GCALE): \(E^TXA+A^TXE=-P_rGP_r\). \(E, A, G\in R^{n\times n}\) are given matrices. \(X=P_1XP_1\in R^{n\times n}\) is an unknown matrix, where \(P_1\) and \(P_r\) are spectral projections onto the left and right deflating subspaces corresponding with the finite eigenvalues of a regular pencil \(\lambda E-A\). Large dense matrix coefficients in the GCALE are supposed. The solution is realized by using the modified matrix sign function method. It guarantees the quadratic convergence for pencils of arbitrary degree. Numerical experiments show this iterative method can be competitive with direct methods for large dense problems.