If a lie is being disseminated; is it the duty of the Imaam of a Masjid to inform his Muqtadien about it (specially if it is such that creates an environment of prejudice and presents an excuse to the perpetrators to inflict injury to the Jamaat)? Or may he (the Imaam) choose to keep quiet because of some perceived or possible threat to him or to the administration of his Masjid?

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.

It is a must on every Muslim who hears or sees a sin or an evil that is considered by the Islamic legislation as such, to change it according to his ability. The Prophet said: "Whoever among you sees an evil, he must change it with his hand (i.e. physically), if he is unable to do so, then with his tongue, and if he is unable to do so, then with his heart (i.e. by hating it), and this is the weakest level of faith." [Muslim] There is no doubt that the Imaam of the mosque is the first person who is obliged to forbid evil with wisdom and appropriate admonition. For instance if slander and backbiting is widespread in the society, or other evils that lead to the division of  Muslims and spoils their unity, the Imaam  should deal with them with wisdom and with appropriate means. Allaah does not burden a soul more than it can bear. This is the principle. But one should know that considering the damage or benefit to change such a rumour (mentioned in the question), and rule that it is an evil or the like, is a matter that the Imaam and the administration of the mosque should deal with as they are more knowledgeable about the situation.      

Allaah knows best.