The LEAN concept of waste is helpful to apply to an analysis of processes. For example, when looking at the functional integration of two similar business units, you can conduct an analysis of current state processes for each unit and identify processes inefficiencies (wastes) that are opportunities to improve overall outcomes when combining the two units into a more efficient, streamlined process.
Value stream mapping is incredibly helpful. It helps understand how the business models creates and delivers value to the customer. The exercise in itself is great way to acclimate and align an integration team to an acquired business model.