Public Service Integrity Act This bill expands the post-employment ban on lobbying by former Senators, former Members of the House of Representatives, and certain former congressional officers and employees. Currently, former Senators are banned from lobbying for two years, while former Representatives are banned for one year. The bill increases the ban to five years. Additionally, current law bans lobbying by former House and Senate officers and staff of Member offices, committees, and other legislative offices for one year. The bill increases the ban to two years. The bill also makes more former congressional employees subject to the post-employment lobbying ban by lowering the income threshold at which the ban applies. Currently, the ban applies to any employee who, while employed by a Member of Congress, earned more than 75% of that Member's basic rate of pay. The bill lowers that threshold to 50% of the employing Member's rate of pay.