All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If this leader is the most competent member of the group in running the organization and achieving its objectives in the cause of Islam, then it is not permissible to endeavour to dismiss him from his position. So we advise you to conceal his sin as the Prophet said: "Whoever conceals the sins of a Muslim, Allaah will conceal his sins on the Day of Judgement." [Al-Bukhari and Muslim]
However, if he is not the most competent member of the organization in running it and achieving its objectives, and there is another member who is more righteous than him, and there is no way for appointing this righteous man except by informing the group that this chairperson lies and swears to a lie, then there is no harm in informing them about it while persisting in advising him and trying to be friendly with him. Your objective in this should be that of pure advice and love of good for everyone, without following one's desires or whispers of the devil.
Allaah Knows best.