"Further care is pending the results of pathology and imaging tests," the A's said in a statement.
Lambo reached out on Twitter Tuesday, tweeting: "Thank you everyone for the prayers and support. I'm truly blessed to have soo much love. I'm going to beat this and be back on the diamond."
The A's placed Lambo on Nashville's disabled list and will provide updates only as they are relevant to his playing status, but the organization expressed its support for him through this process.
"The A's are incredibly grateful to the doctors at Vanderbilt for their excellent care in Andrew's case," A's general manager David Forst said in the release. "In coordination with our team physician, Dr. Allan Pont, they have provided Andrew with first-class treatment as he fights this disease. I let Andrew know that his health is of the utmost importance to us and that the A's will assist him in any way possible through his treatment and recovery process."
Lambo, who turns 28 in August, joined the A's via waivers in November and made the Opening Day roster, appearing in one game before being optioned to Nashville, where he was hitting .255 with four home runs and 30 RBIs.
A's manager Bob Melvin said, "We all have our fingers crossed for him."
"He's a pretty gregarious guy," Melvin continued. "Fits in well in the clubhouse. At some point in time we figured we'd see him this year. Right now what he has going on is a lot more important than that. So our thoughts and prayers are with him."
Jane Lee has covered the A's for MLB.com since 2010. This story was not subject to the approval of Major League Baseball or its clubs.