Extending is for sure the best option. This is built into the rules with the day extending five minutes after each vote. A longer extension is also fine, but if it really comes down to a tie, No Lynch fits the best thematically. If you have a group of people arguing late into the night with a deadlocked vote, you don't decide who to kill based on information unknown to you, you don't flip a coin, you go home and try again tomorrow.