Lincoln High School is the infected-filled school at the end of Bill's Town, where Joel, Ellie and Bill go looking for a military truck's battery. The High School Escape section and a bloater fight in the gym happen here.
A military truck sent for supplies was swarmed by infected and crashed into the school. Only the military still made car batteries, so Joel needs the one in that truck to get a vehicle running.
The battery is already gone. You fight through the halls to the gymnasium, kill a bloater and a group of runners with Bill and Ellie, and escape to a nearby house.
Frank took the battery and used it to fix a pickup in a house nearby. He was bitten in the process and killed himself there, leaving the working truck in the garage for Joel and Ellie.