I downloaded and installed Cubase AI8 that came with my Motif XF6 on my 2006 MacBookPro Version 10.7.5, but will not work because cubase AI8 requires at least 10.8 or later. I cannot update my OS anymore, 10.7.5 is the maximum my MAC can work it. 

Will Cubase issue me another download if later in the future I buy another MAC ?

I think you can activate it on another PC/Notebook too.
However, you must deactivate it on the old one first.
(As far as I know.)

I wanted to do it on my new PC (installed it on a tablet first),
but I wasn’t able.
But I switched to Studio One 3, so I didn’t really care about Cubase anymore.

You can download AI7 from the Steinberg website and it will run using the AI8 license.

Speaking of license, I have both unused copies of AI4 & AI5 from Yamaha gear like my CP1 and my Tyros 5. I tried to load both copies but I can’t find either of the 25 digit codes. They didn’t bother to put the codes on the sleeves so although they are brand new sealed, I can’t use them. I have another copy straight from Yamaha which has some coded lettering on the sleeve but nothing that appears to be a 25 digit access code. I emailed Steinberg and got no reply thus far.