Lithographic printing plate are formed by imagewise exposing a positive-working lithographic printing plate precursor with infrared radiation to form an imaged precursor comprising exposed regions and non-exposed regions, and processing the imaged precursor to remove the exposed regions using a processing solution having a pH of 12 or more, that contains a metal cation M2+ selected from barium, calcium, strontium, and zinc cations, and is substantially silicate-free. The positive-working lithographic printing plate precursor comprises a grained and anodized aluminum-containing substrate, a first ink receptive layer comprising at least one water-insoluble, alkali solution-soluble or -dispersible first resin, a second ink receptive layer disposed over the first receptive layer, and an infrared radiation absorber in an amount of at least 0.5 weight %, in either or both of the first ink receptive layer and the second ink receptive layer.