No, Acrobat 7.0 Standard was a prety old softwre and will not run on MAC 10.7.4. You need to switch to new version of Acrobat which is XI that will work just fine on your MAC Lion.
Acrobat X is not available any more, so, you won't be able to upgrade as well. To get Acrobat XI upgrade, you need to have atleast Acrobat 8.0.
The best option for you will be to get a full version of Acrobat XI from adobe.com or can get the subscription for Acrobat XI Pro
You can check the prices from the below link.