Turbotax for 2016 will apparently require 10.9 or higher. It may install and run on less, but any problems caused by the old system will not be fixed or guaranteed.
Your options would be to use turbotax online via a web browser, or buy or borrow a Mac or PC to install with the desktop version. The PC version will still run on Win 7, the requirements are more forgiving. Or, use Parallels or Bootcamp to run Windows on your Mac (I think that was available as long ago as 10.7, although I didn't use it back then.)