Herbert started against the Kansas City Chiefs in place of Taylor, who was taken to hospital after suffering a chest injury before the game.
"I'm gonna wait and see what type of health Tyrod is in," Lynn told reporters after falling to the Chiefs in overtime when asked about his quarterback situation, according to ESPN's Alden Gonzalez. "If he's 100% ready to go, he's our starter. But I know Justin can pick up the slack."
Lynn revealed he didn't find out about Taylor's unavailability until after the opening coin toss. Herbert said he didn't know he was starting until seconds before kickoff.
In his first career game, Herbert completed 22 of 33 passes for 311 yards against the defending champions with one touchdown and one interception. He also rushed for a touchdown, though the Chargers lost 23-20 in overtime.
"Whether I'm the guy next week or not, I'm going to prepare like I am," Herbert said, according to AJ McCord of KOIN News. "I know I belong out here."
Herbert was the sixth overall pick in the 2020 NFL Draft. The Chargers planned to groom him for a year behind Taylor, who led the Chargers to victory over the Cincinnati Bengals in the season opener.
The Chargers will take a 1-1 record into a Week 3 meeting with the winless Carolina Panthers.