Unfortunately, factory warranties are limited - in your case, 4 years for 50,000 miles -- or 6 years / 70,000 miles powertrain. Beyond that, the warranty has expired. That is why a water pump replacement would not be covered.
RepairPal Certified shops can diagnose and repair your 2016 Lincoln MKS. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.