Donald Sterling's Doctor -- I Didn't Lie to Him

Donald Sterling knew full well he was being tested for Alzheimer's when a doctor examined him last month ... but it's unclear if Donald knew his control over the L.A. Clippers was on the line.

TMZ Sports has obtained a letter written by the examining doctor to Shelly Sterling's lawyer, Pierce O'Donnell. According to the letter, the doc met Donald at his house on May 22. Shelly was also present.

After the exam the doctor concluded Donald's mind was impaired by the disease, to the point he was "at risk of making potentially serious errors of judgment, impulse control, and recall in the management of his finances and his trust."

Here's what's murky. It's unclear if Donald knew he was being examined for the purpose of determining if he should be stripped of control over the team. The doctor explains Sterling had previously been examined by a doctor at Cedars-Sinai Medical Center who concluded he had Alzheimer's, and the doctor was there for a second opinion.

The doctor writes, "I asked him if he knew why I was there, and he said, 'I think so.'"