The team placed him on injured reserve Monday.
Lamp was making his second career start at left guard when the injury occurred during the second quarter of the 23-20 loss. The third-year lineman, who was a second-round pick in 2017, has been plagued by injuries throughout his career.
Dan Feeney moved from center to left guard and Scott Quessenberry played center. Coach Anthony Lynn said Monday that Ryan Groy also could be in the mix at either center or guard. Groy was signed on Oct. 9 after Mike Pouncey was placed on injured reserve following a neck injury.
Los Angeles (2-5) has lost three straight games going into this weekend's game at Chicago.
The Associated Press contributed to this report.