A method is used to prepare lithographic printing plates by developing positive-working lithographic printing plate precursor that has a single imageable layer that comprises a polymer binder having recurring units represented by Structure (Ib) below: wherein the recurring units of Structure (Ib) are present in an amount of at least 25 and up to and including 60 mol %, all based on total recurring units in the polymer binder, and R2 is a substituted or unsubstituted hydroxyaryl group in which the hydroxyl group is ortho to the ester linkage, to form exposed and non-exposed regions in the imageable layer. The resulting imaged lithographic printing plate is developed using a silicate-free developer composition having a pH of at least 12 and comprising at least 0.001 gram-atom/kg of a metal cation M2+ selected from the group consisting of barium, calcium, strontium, and zinc cations.