What is the old testament festival in which the lords supper was instituted?

The spring Feasts Commonly called Passover.. which started on the 14th of the month of Nisan.. (Passover feast), then the feast of (Unleavened Bread) on the 15th.. and ends with the (feast of First fruits) which occurs on the first day after the Sabbath after unleavened bread... a Sunday...

*Note that during the passover meal there were 4 cups that were served...

The first cup was celebrating the call of the people of God in Abraham, the second was the celebration of the deliverance of the nation in Moses, the third cup celebrated the forgiveness of sin in the coming Messiah, and the forth cup celebrated the promise of God to gather his people to Him in the future forever.. also note that during the passover meal at the third cup.. Jesus stood up and declared himself as the Messiah and established the "Lords Supper" and His statement that he would not drink of the cup again until He drinks it with us in Heaven, (the fourth Cup). See Matthew 26:27-29.