Methods and systems for producing fluids from a subterranean well include forming the subterranean well having at least one lateral wellbore. The lateral wellbore is completed with a lateral production tubular. The lateral wellbore is subdivided into subsequent lateral segments. Each lateral segment is defined by a downhole lateral packer and an uphole lateral packer that seal an annular lateral space defined by an outer diameter surface of the lateral production tubular and an inner diameter surface of the lateral wellbore. A main production tubular extends into the subterranean well, the main production tubular including a lateral access system that provides selective access to the lateral wellbore. A flow of a fluid within the lateral segment is controlled with an inflow control device of the lateral segment. The inflow control device is mechanically adjusted by a tool that is delivered to the inflow control device through the lateral access system.