Complex sentence: After Lanois finished a stage of the production work with U2, Robertson let Lanois know that he was ready to begin, and the two began production and recording for Robertson's album in July of 1986.
Split into simpler sentences: After Lanois finished a stage of the production work with U2, Robertson let Lanois know that he was ready to begin. The two began production and recording for Robertson's album in July of 1986.