The Trump administration claimed that Mike Flynn was fired because he lied to the Vice President about the discussions that he had with the Russian Ambassador during the Trump transition. The story is more complicated than that. Flynn was warned to avoid having contacts with the Russian Ambassador by the Trump transition team. He was told that the FBI was undoubtedly monitoring the ambassador's phone calls. That should not have surprised him because he had a top security job in the military before being appointed to his job in the Trump Administration. Flynn ignored the advise he was given. An intercepted phone message by the FBI found that Flynn was discussing the sanctions imposed on Russia by the Obama administration. Obama ordered the sanctions after determining that Russia had been taking actions to influence the US election. There was no way that Flynn could remain in his job after the content of his discussions with the Russian Ambassador were captured by FBI surveillance.
Donald Trump accused the Obama administration of taping his phones at the Trump Tower. Flynn was at the Trump Tower with Trump's son-in-law during a phone conversation with the Russian Ambassador in which the Obama sanctions were discussed. The Russian Ambassador's taped phone provided the information about Flynn's conversation. There was also a lot of conflict in the Trump transition team that might have influenced Flynn's behavior. Some were cautious about taking a soft position on Russia, and others wanted to make good on Trump's claim that he would improve our relationship with Russia. Flynn was obviously part of the soft on Russia team.