Is the phrase "The ends justify the means" a concept favored in Judaism? For instance, can one lie in order to get others to perform a Mitzvah?
It will depend on the case, Judaism takes a balanced approach to this issue. Judaism definitely does not subscribe to the absolutist position of Deontologists such as Kant that the ends never justify the means. Kant would say that one could never lie, even to save someone else. However, in Judaism, every sin except 3 is nidcheh if there's any danger to life.
There are also more complex cases where the ends may justify the means. For example, Chazal say that when Aharon haKohen saw 2 people were in a fight, he would approach each one of them and say that the other was sorry for having wronged the other, but was too embarrassed to come forth and say so. Although he wasn't being fully honest, this way he would help bring reconciliation among the Jews, and is praised for it (see Malachi 2:5-7). Lying is a social wrong, but its not a clear-cut prohibition in all cases. So in cases where its for the greater social good of the people involved, it may be praiseworthy. However, one must carefully evaluate the circumstances to see if good will really come from it. Tricking people to get them to do a mitzvah might lead to a chilul haShem later on, so it will depend on the case.
Aharon's love for the Jews and willingness to 'sin' for the greater good sometimes went too far. I.e. Aharon went along with their plan to create the Golden Calf. Chazal explain this was too prevent the Jews from going too far in sin and possibly killing him, the Kohen and prophet. Yet even so, God is extremely critical of Aharon for this, and only Moshe's intercession saves him (See Devarim 9:20). This is because Idolatry is such a serious sin, no "end" can justify committing it.
Chazal also discuss the case of Yael, where she seems to have seduced the enemy general, Sisera, and then killed him. They say "gadol avirah lishma m'mizvah shelo lishmah" (Horayos 10b). So in certain circumstances, even a complete sin may be allowed so as to save the Jews. However, Yael may not have even been Jewish, and this dictum is not applied elsewhere. So as a general rule, a direct biblical prohibition can only be violated to save a life, while a lower social wrong can be allowed for the greater good.
An example of the ends justify the means in Judaism is makos mardus: although the means (hitting someone) is repugnant, we do so because of the end, which is the retention of a civil, Torah-observant society.