I don't know of a good way to spot which application has raised the dialog box, except via the menu bar. If you've selected the dialog box, see if the name of the application associated is up in the menu bar.
Otherwise... What login items are present? System Preferences > Users & Groups > Login Items. Other than maybe iTunesHelper, hover over the application name to get the path to the application, and then remove the entries you don't use or don't recognize, log out and log back in, and see if the prompt goes away.
Otherwise, open Console.app from Applications > Utilities, and see if you can find a server connection error logged there. There'll be a lot of messages there and some will be quite arcane or maybe even ominous, and that deluge of text can be perfectly normal. You're specifically looking for a server connection error with a timestamp around the time that dialog box pops up.
If you can't resolve this from the above steps, then download and run Etrecheck, and post the diagnostic report here, and maybe somebody can spot a package that's raising this dialog box.
OS X 10.7.5 is far enough back that there can be problems with establishing secure connections, but that's a complete guess. If your Mac supports it, consider an upgrade to a newer version of OS X.
Antivirus and Anti-malware packages have a long and sordid and increasingly questionable history, and its efficacy lately — per the industry itself — has been rather below 50% (and I'd suspect, dropping), and the software has caused more than a few issues with stability and reliability. Most folks with OS X get bagged by installing the malware themselves, or through what's known as phishing; trying to get the user to install the malware, or to open up access to the system to allow the attacker to log in and install the malware.
Keep Gatekeeper set to allow only App Store and identified developers (System Preferences > Security & Privacy), and configure and keep Time Machine or some other backup tool running, and don't install anything you didn't go looking for. I'd likely also either disable or remove Microsoft Silverlight, Adobe Flash and Oracle Java, or minimally keep them current and get a plugin blocker, as these are the some of the most common paths for the junk to get onto a system, if it's not directly installed by the user.