James is receiving a second opinion on the injury, a source told ESPN's Adam Schefter.
The Chargers, in saying that James would be evaluated, said a time frame for his return has not yet been established.
"I like the depth that we have in our secondary," Lynn said, dismissing the possibility of adding Earl Thomas.
It's another injury setback for James, a talented young safety who is entering his third season in the NFL.
James suffered a Jones fracture in his right foot last August and didn't appear in a game until Week 13
Drafted No. 17 overall in 2018, the Florida State product played in all 16 games his rookie season. James led the Chargers in tackles (105) and posted 3.5 sacks, three interceptions and 15 pass breakups, earning All-Pro and Pro Bowl honors.
ESPN's Alden Gonzalez contributed to this report.