alexandrite

how does one determine the difference between a natural alexandrite,& a lab created one, or a color changing sapphire?

If your lab created alexandrite had the same chemistry down to trace elements as alexandrite, you'd be looking for inclusions and growth patterns. Once you've seen one of these sapphires, you'll never confuse them. There's a purply pinky for the green and a wine purple for the red. A gemologist would give you a better answer.