I got many answers to this puzzle, and there was a very good response. Most of you answered the puzzle correctly. The first ones I got correct were from Anku Jain and Sid Pareek.
The correct answer is Tuesday.
Here is the correct answer (Sorry no video this time, traveling currently without an iPad), I am reproducing the one from Anku Jain without any changes – thanks Anku!
1) Both Day 1 and Day 3 cannot be a lie. If it were so, there would be at least 2 true days.
2) This means Day 2 is a lie for sure. So, this day has to be one of Mon, Tue, Wed, Fri
3) Now, if Day 1 is true, it has to be Wed or Fri (because Day 3 is a lie). However, either Wed or Fri is not possible because of the types of days possible on the next day.
4) This means Day 3 is true. It cannot be Mon because of previous day constraint. So, It has to be Tues.
Hope you enjoyed the puzzle!