You can file a lawsuit under 1447(b) as soon as the 120 day deadline passes. You would only have to demonstrate that 120 days have passed since your interview and no decision has been made.
You probably read about the writ of mandamus (WOM) lawsuit. Several years ago, there were countless cases involving applicants getting stuck in the FBI name check process, sometimes waiting years to get an interview. Since no interview was conducted, these applicants were ineligible to file a lawsuit under 1447(b). The only recourse available to them was WOM. The purpose of filing a WOM is to get the courts to compel a government agency to do its job (in this case, to adjudicate a naturalization application in a timely manner). In order to successfully file a WOM, the applicants needed to provide proof to demonstrate that they made every reasonable effort to resolve their case via administrative channels (InfoPass, inquiring with elected officials, etc.).
Although an applicant whose 120 day deadline expired and no decision has been made and/or no oath letter has been issued is eligible to seek legal recourse under 1447(b), it's still a good idea to begin contacting the USCIS and various elected officials in an attempt to resolve the case administratively. Chances are that an application may be sitting on someone's desk, forgotten, and they just needed a swift kick in the behind to force them to remember it.
