Mat 26:19 And the disciples did as Jesus had appointed them; and they made ready the passover.
Mat 26:20 Now when the even was come, he sat down with the twelve.
Mat 26:21 And as they did eat, he said, Verily I say unto you, that one of you shall betray me.
Jesus said He would keep the passover at a house...The disciples procured the house and made ready the passover...That would include preparing a real lamb...They ultimately sat down at the house where the passover meal had been prepared and ate the meal...
You do realize that preparing for the Passover took, in most cases....one full day. In some others....two days. Passover preparation began at the sundown of the 13th and continued the entire day of the 14th. The lambs were killed in the temple "Between the Evenings" (noon and sundown) on the 14th. This was the exact time Our Lord was killed also.
When He told them to find a room for the feast they did not yet realize that He would be dead when the lamb was eaten. The Days of Unleavened Bread continued for another seven days after Passover Preparation [Leviticus 23:6] and it would have been normal for Him to provide a place for them for the observance. The Passover, itself....was eaten at the cusp of the 14th and the 15th.....24 hours after the Last Supper.
Notice [John 13:29] For some of them thought, because Judas had the bag, that Jesus had said unto him, Buy those things that we have need of against the feast; or, that he should give something to the poor. Why would The Lord send Judas out to buy what was needed for the Feast (Passover) if they had all just eaten it? The lambs would be sacrificed the following afternoon and the Feast would occur 24 hours later while Our Lord would be spending His first night in the tomb.
The Last Supper was not a Passover Meal....it was a Supper.