The LCLS photocathode rf gun requires a solenoid immediately downstream for proper emittance compensation. Such a gun and solenoid have been operational at the SSRL Gun Test Facility (GTF) for over eight years. Based on magnetic measurements and operational experience with the GTF gun solenoid multiple modifications are suggested for the LCLS gun solenoid. The modifications include adding dipole and quadrupole correctors inside the solenoid, increasing the bore to accommodate the correctors, decreasing the mirror plate thickness to allow the solenoid to move closer to the cathode, cutouts in the mirror plate to allow greater optical clearance with grazing incidence cathode illumination, utilizing pancake coil mirror images to compensate the first and second integrals of the transverse fields and incorporating a bipolar power supply to allow for proper magnet standardization and quick polarity changes. This paper describes all these modifications plus the magnetic measurements and operational experience leading to the suggested modifications. Show Partial Abstract