Hello nichken,
Thank you for using Apple Support Communities.
I understand you cannot find the Mac App Store application on your OS 10.7.5. That application would have come with that version of OS X, but it may have been removed from the Dock or otherwise hidden. If you take a look at this information:
If the Mac App Store application was removed after installing the Mac OS X v10.6.6 Combo Software Update
First, confirm that you haven't simply removed the App Store icon from your Dock:
Open the Finder.
Choose Applications from the Go menu.
Locate App Store in the Applications folder.
If you cannot find the app, confirm that it isn't in your Trash by clicking on the Trash icon on your Dock and looking for App Store in the Trash contents. If it is listed in the Trash contents, follow the steps in this article under Step 1, "If you change your mind..." to return the App Store to your Applications folder.
If the Mac App Store has been fully removed from your computer, visit AppleCare Support Downloads to download the Mac OS X v10.6.6 Combo Software Update package. Double click the file that downloads to run the Software Update. The Mac App Store will be replaced in the Applications folder and in your Dock.
From this article:
Troubleshooting the Mac App Store - Apple Support
Whie this article addresses OS X 10.6, the outlined steps and instructions would also apply to OS X 10.7.5.
Regards,
Jeff D.