The version of AirPort Utility that you are using with Lion 10.7.4 does not have logging capabilities.
If you are still running Lion 10.7.4, you do have the option to install and use AirPort Utility 5.6, which does have some basic logging functions.
AirPort Utility 5.6 for Mac OS X Lion
You can keep both AirPort Utility 5.6 and 6.x on your Mac and use the version that you need.
To see the logs in AirPort Utility 5.6....
Open Macintosh HD > Applications > Utilities > AirPort Utility 5.6
Select the Time Capsule and click Manual Setup
Click the Advanced (gear) icon
Click Logs and Statistics
Click Logging and Statistics again
If you have upgraded to Mountain Lion 10.8.x, unfortunately there is not a version of AirPort Utility that will display log information in that operating system. We do not know if Apple plans to provide this function or not.