Sources tell ESPN's Adam Schefter that Lamp is expected to miss the season.
Lamp suffered the injury while pulling on a running play during team drills.
After being attended to by trainers, the Western Kentucky product had to be carted off the field but was seen limping on his own to the team training facility at Jack Hammett Sports Complex and putting some pressure on his right leg.
"He was playing so well," Chargers coach Anthony Lynn told reporters after practice, before the extent of the injury was known. "He was really coming along at that right guard position. He was playing really well, so it will definitely hurt this team."
Injuries handcuffed the Chargers last season, and the franchise appears headed down a similar path at the start of training camp in 2017.
The Chargers are already without the services of another rookie, wide receiver Mike Williams, who was shut down for the duration of training camp as he rehabs from a lower back disk herniation.
According to ESPN Stats & Information, the Chargers finished with 27 players on the injured reserve last season, second-most in the NFL.