I think I see what you’re saying now, but the way you said it confused me. Remember that there was not just one original lamb, but one lamb per household. Based on the population data given in the Pentateuch, that’s a lot of lambs!
You are right that when the Israelites ate the Passover, they were not eating any of the lambs from the first Passover. They were eating new lambs. But that does not necessarily have any bearing on the Eucharist and the Last Supper. Catholics do not see the mass as just another celebration of the Passover, otherwise we would only go to Church on Easter. The Passover was only a foreshadowing (or type) of the Lord’s Supper. The blood of the lambs didn’t have any power of themselves to purify from sin and avert God’s judgment. For that reason, the identity of the individual lamb sacrificed didn’t matter. The forgiveness of sins came entirely through Jesus Christ, who is not any lamb but the Lamb of God. The Eucharist then is not just another Passover meal anymore than the lambs sacrificed in the Passover could be literally identified as Christ. It is a new rite entirely. In that he saith, A new covenant, he hath made the first old. I propose it is more fitting that the old rite, which was only symbolic, had a symbolic memorial, and the new rite, which is based on the true forgiveness of sins by the blood of Jesus Christ, out to be a true memorial, not just the presence of bread and wine, but the Bread from Heaven and the fruit of the True Vine, which is the cup of his blood.
Not only is the Eucharist not identical with the Passover, it is not foreshadowed only by the Passover either. A few obvious examples would be the showbread, the manna and the offering of Melchizedek. So when you say the Passover is celebrated once a year, that is true, but they ate manna every day. So while we celebrate Easter once a year, we celebrate mass daily. It also explains why the gifts of the mass are bread and wine rather than a lamb (though it would make church more exciting).
Regarding eating the lamb, you are correct that spreading the blood on the door was the most essential part of the sacrifice (the oblation). Nevertheless, it would not be right to say that eating the lamb in no way belonged to the sacrificial act anymore than it would be right to say the same thing about slaughtering the lamb. In the Tabernacle, after the blood is sprinkled, the body of the victim is consumed (immolation). Eating the lamb was the form of immolation for the Passover sacrifice, which is seen clearly in the fact that what is not eaten by morning is commanded to be burnt (Ex. 12:10).
