Office 2004 is not compatible with Lion or Mountain Lion because they don't include the Rosetta software that allowed PPC apps to run on Intel hardware.
Office 2008 was the first version of Office designed to run natively on Intel chips.
Office 2011 is the current version.
You can update to Office 2011, Office 2004 was introduced 9 years ago. You can use other 3rd party softwares, i.e., iWorks, Office Libre, etc., that are capable of handling Office documents.
Or, you can revert back to Snow Leopard.
All in all, this topic has been covered in these forums almost every day since Lion was introduced 2 years ago.
Please search the forums for more info.