Lacy, who has started 21 games during his college career, was the team's top reserve at both the guard and tackle positions.
An MRI revealed the injury after Lacy felt discomfort during Tuesday's practice.
"I feel for him," Mora told reporters Thursday. "He's a senior, he's worked hard, and he's put himself in a position to compete. He's a great kid. ... You just hate to see that happen.
"The human body is a mystery in terms of how it's going to heal, so you just don't know. So we don't like to put timelines on guys. I said he was out for the season, but they might go in there and he might have a miraculous recovery and be back, so we'll see."