Turbotax 2015 requires OS 10.9 or higher.  If it install on 10.7, any problems you have won't be supported.

Your install file needs to be a .dmg file (disk image).  If it is an .exe file, you have the PC version by mistake.

When you open the .dmg file, it should open a virtual disk window containing the application; that application needs to be dragged to your applications folder, then restart your mac to dismount the virtual disk.  Running turbotax from the .dmg file or the disk image doesn't work.

You also need to be logged into an administrator account.

You may need to remove fragments of past partial installations.  See below to remove all the hidden files and folders, then reinstall just what you want.

https://ttlc.intuit.com/replies/3301991