Hello Daq,
The reason there was no lamb at the last supper is because it was not the Passover, the Messiah was slain the following day on the day of the Passover sacrifice, so how could he have a lamb on the table the night before?
It was a sin before God to refuse to partake of the Passover at the proper legal time:
NAS
Numbers 9:13 'But the man who is clean and is not on a journey, and yet neglects to observe the Passover, that person shall then be cut off from his people, for he did not present the offering of the LORD at its appointed time. That man shall bear his sin.
Yeshua greatly desired to partake of the Passover with them (before his suffering) but he knew that his suffering and would come
before they would be together to eat it:
NAS
Luke 22:15 And He said to them, "I have earnestly desired to eat this Passover with you before I suffer;
NAB
Luke 22:16 for, I tell you, I shall not eat it (again) until there is fulfillment in the kingdom of God."
The NAB translation adds the word (again) in the parenthesis to show it is not in the original Greek. The English translators who all followed Rome’s teaching that the last supper was the Passover all insert this word, or something like it, to show that Jesus did of course eat it this night, but will not “again” eat it.
But the Messiah states very clearly that he will
not eat it, until it is (spiritually) fulfilled in the Kingdom of God. He expresses great desire to eat it, but then says clearly that he will not eat it, because he knows he will no longer be with them at that time, his suffering would come before the time to eat it.
This chapter lists over 50 reasons why the last supper was not the Passover:
http://themessianicfeast.com/wp-content/uploads/2015/01/TMF_50-Reasons.pdf
This is also why they are not ashamed to tell all Jerusalem and the whole world that they and the Messiah are all eating “bread” at this meal, because it was not the Passover, so bread was perfectly legal.