Are you required to disclose medical conditions to your flight instructor?
When it comes to the AME, you must disclose everything fully and completely.  Failure to do so may void any license and insurance and expose you to extraordinary civil and criminal risk.

When it comes to your flight instructor, who is not a medical professional, you do not need to disclose the specifics of your situation.  Saying, "I have concerns about passing a Class III Medical Exam due to certain conditions" is sufficient, and is not the same thing as lying.  Do not claim you are healthy when you know you are not.

Your instructor may decide not to continue training until a physical is passed, or he may decide just to be a little extra vigilant during training, and delay certain elements or maneuvers depending on the information you choose to provide.

For example: If you choose to disclose vertigo problems, he may avoid steep turns until medical clearance.  If you choose to disclose vision issues, he may avoid night-flight.

Regardless, you will need a medical before your first solo flight.

Do not lie to your instructor, but that is not the same thing as disclosing full details of your health with a non-medic.