A stable formulation of dual Lanczos tridiagonalization of non-Hermitian matrices, along with solution of tridiagonal systems of equations, is used to simulate liquid nuclear magnetic resonance (NMR) spectra for systems with chemical exchange. The method provides computer storage and performance advantages over our previously developed sparse-matrix methodology [Dumont, Jain, and Bain, J. Chem. Phys. 106, 5928 (1997)], in addition to the incorporation of full blocking of the system Liouvillian with respect to the conservation of z magnetization. Convergence with respect to number of Lanczos iterations is investigated in some detail in order to achieve optimal performance.