The upgrade from Mac OS 10.7.5 (Lion) to 10.8.6 (Mountain Lion) was a paid upgrade, so it won't show as something you can download. All the upgrades after Mountain Lion have been free, but not all Mac systems can be fully upgraded. There are free ways to upgrade from Lion to something higher, but it can be a bit tricky and the ultimate version that can be installed depends on your hardware.
Helping you upgrade your mac system is not really a function of this board. If you can upgrade your Mac, you will be able to install from the CD. The download version has the same requirements and can't be installed unless you upgrade your Mac.
If you don't want to, or can't upgrade, or can't upgrade in time, you will either have to borrow another Mac, borrow a PC to install Turbotax on, or switch to using the web browser version. Since you already paid for the CD version and the web browser version is payable online when you file, you can either return the CD where you bought it, or contact customer support about a refund, or use the Satisfaction Guarantee to get a refund for the CD.
The Satisfaction Guaranteed policy and claim form are here.
https://ttlc.intuit.com/replies/3301962
