Gimbal Lock Problem

Hello everyone, I have this problem with Quaternions, I tried to pass the rotation of some objects to the rotation of one object, but at some angles I get the Gimbal Lock problem, like when the X rotation is 90, the Y rotation rotates on the Z axis, this is the code:

 switch (axis) 
         {
             case Axis.X:
                 switch (typeOfEditing)
                 {
                     case EditType.Rotation:
 
                         if (oldRotAxis != transform.localEulerAngles.x)
                         {
                             newRotAxis = transform.localEulerAngles.x - oldRotAxis;
 
                             objToMove.localRotation = Quaternion.AngleAxis(newRotAxis, Vector3.right) * objToMove.localRotation;
                             follower.localRotation = Quaternion.Euler(newRot);
                             oldRotAxis = transform.localEulerAngles.x;
                         }
 
                         break;
                 }
                 break;
             case Axis.Z:
                 switch (typeOfEditing)
                 {
                     case EditType.Rotation:
 
                         if (oldRotAxis != -transform.localEulerAngles.x)
                         {
                             newRotAxis = -transform.localEulerAngles.x + oldRotAxis;
 
                             objToMove.localRotation = Quaternion.AngleAxis(newRotAxis, Vector3.forward) * objToMove.localRotation;
                             follower.localRotation = Quaternion.Euler(newRot);
                             oldRotAxis = -transform.localEulerAngles.x;
                         }
 
                         break;
                 }
                 break;
             case Axis.Y:
                 switch (typeOfEditing)
                 {                    
                     case EditType.Rotation:
 
                         if (oldRotAxis != transform.localEulerAngles.y)
                         {
                             newRotAxis = transform.localEulerAngles.y - oldRotAxis;
 
                             objToMove.localRotation = Quaternion.AngleAxis(newRotAxis, Vector3.up) * objToMove.localRotation;
                             follower.localRotation = Quaternion.Euler(newRot);
                             oldRotAxis = transform.localEulerAngles.y;
                         }
 
                         break;
                 }
                 break;
         }

Is there a method, to apply a rotation to each axis and evading the Gimbal Lock? I have tried also the Quaternion.Euler but gives me the same results.