The Lewinsky matter came about because of the Paula Jones trial. Paula's attorneys are the ones that grilled Clinton on Lewinsky, and Clinton perjured himself.
From Wikipedia: Jones's lawyers decided to show to the court a pattern of behavior by Clinton that involved his allegedly repeatedly becoming sexually involved with state or government employees. Jones's lawyers therefore subpoenaed women they suspected Clinton had had affairs with, one of whom was Monica Lewinsky. In his deposition for the Jones lawsuit, Clinton denied having "sexual relations" with Monica Lewinsky. Based on testimony provided by Linda Tripp, which identified the existence of a blue dress with Clinton's semen on it, Kenneth Starr concluded that Clinton's sworn testimony was false and perjurious.
During the deposition in the Jones case, Clinton was asked, "Have you ever had sexual relations with Monica Lewinsky, as that term is defined in Deposition Exhibit 1, as modified by the Court?" The judge ordered that Clinton be given an opportunity to review the definition. It said that "a person engages in sexual relations when the person knowingly engages in or causes contact with the genitalia, anus, groin, breast, inner thigh, or buttocks of any person with an intent to arouse or gratify the sexual desire of any person".[28][29][30] Clinton flatly denied having sexual relations with Lewinsky.[31] Later, at the Starr Grand Jury, Clinton stated that he believed the definition of sexual relations agreed upon for the Jones deposition excluded his receiving oral sex.
It was upon the basis of this statement that the perjury charges in his impeachment were drawn up. The House of Representatives voted to impeach Clinton on December 19, 1998, on charges of perjury and obstruction of justice and sent the case to the Senate for trial.
Which is why we stay away from perjury traps!