According to the Qur'an or Hadith, is it permissible for a Muslim to lie in some circumstances?
If so, under what circumstance may a Muslim lie?
Lying is forbidden except in three instances, and they are:
To please ones wife
lying during/in war
and to try to bring people together
Lying outside of these three (exceptions) is haram/forbidden. Furthermore I would like to point out that even if a lie is told in these three situations, it shouldn't be a lie that brings trouble and problems, in other words be harmful.
And concerning the second exception "lying in/during war" an example for it would be if a leader would be taking his army to war, he would conceal information of the place of battle from the enemy by outright saying that we are going to go to "such a place" but go to another but concealing that information. And I would like to point out that the one who tells a lie for instance to bring people together and fix problems between them, he/she isn't considered a liar:
ليس الكذاب الذي يصلح بين الناس فينمي خيرًا، أو يقول خيرًا
'The person who (lies) in order to conciliate between people is not a liar, when he conveys good or says (something) good
May Allah forgive my mistakes.