No, the psassiver lambs were killed at the same place where the Passover Seder was eaten::
"Then Moses called for all the elders of Israel, and said unto them, Draw out and take you a lamb according to your families, and kill the Passover" (Ex.12:21).
The same day as what?
It is also obvious that this day happened before the Passover and thus before the first day of "the feast of unleavened bread":
"And the first day of unleavened bread, when they killed the passover, his disciples said unto him, Where wilt thou that we go and prepare that thou mayest eat the passover?" (Mk.14:12).
So it is obvious that the words "feast of" in this verse were added in error:
"Now the first day of the feast of unleavened bread the disciples came to Jesus, saying unto him, Where wilt thou that we prepare for thee to eat the passover?" (Mt.26:17).
Are you willing to argue that the Lord Jesus actually meant to say the words "feast of" at Matthew 26:17 knowing that would cause much confusion? I say that is impossible and therefore the translators of the KJV made an error when they added those words.
So are you saying that this verse is referring to the day before the Passover?
"And it was the preparation of the passover, and about the sixth hour: and he saith unto the Jews, Behold your King!" (Jn.10:15).
If your answer is "yes" then how do you explain the fact that by that day the Lord Jesus had already eaten the Passover with His Apostles? Here is an explanation of the meaning of the phrase "preparation of the Passover" written by Sir Robert Anderson:
"But does not St. John expressly state that it was "the preparation of the Passover," and must not this necessarily mean the fourteenth of Nisan? The plain answer is, that not a single passage has been cited from writings either sacred or profane in which that day is so described; whereas among the Jews "the preparation" was the common name for the day before the Sabbath, and it is so used by all the Evangelists. And bearing this in mind, let the reader compare the fourteenth verse of the nineteenth chapter of St. John with the thirty-first and forty-second verses of the same chapter, and he will have no difficulty in rendering the words in question, "it was Passover Friday" (Anderson, The Coming Prince [Grand Rapids: Kregel Classics, 1957], 112-113).
This is a valid argument since it is obvious that they had already eaten the Passover by the time of John 10:15. Otherwise, you will have to argue that the night before the events of John 10:16 the Lord Jesus did not eat the Passover with His Apostles. Are you willing to argue that?