Within the context of Exodus 29:38 – 46, allow me to quote verses 38 – 39 and 42 – 43 using the Good News Bible:
“Every day for all time to come, sacrifice on the altar two lambs, one year old. Sacrifice one of the lambs in the morning and the other in the evening.”

“For all time to come, this burnt offering is to be offered in my presence at the entrance of the tent of my presence. That is where I will meet my people and speak to you. There I will meet the people of Israel, and the dazzling light of my presence will make the place holy.“

The first part of this Tamid Sacrifice begins each morning with a male lamb. The priest slaughters the lamb and places it on the fire as the first sacrifice of the day on the third hour. The lamb burns on the fire all day – a continual burnt sacrifice.

Until the evening sacrifice, the priest places every other sacrifice they make on top of the wood where this lamb is burning.

These sacrifices included:
1) The Sin Sacrifice
2) The Guilt Sacrifice
3) The Burnt Sacrifice
4) The Meal (grain) Sacrifice
5) The Peace Sacrifice

At the ninth hour the day’s service ends. When the priest completes all the sacrifices for that day, they finish it with the second lamb. They slaughter it and place it on top of the day’s offerings.

This creates a sandwich, enclosing all of the day’s sacrifices between the two lambs of the Tamid Sacrifice

According to ancient Jewish sources outside the Bible, the morning sacrifice/offering of the Tamid took place at 9 a.m. The evening sacrifice/offering took place at 3 p.m.

(See Mishnah, Tamid 3:7; Josephus, Antiquities 14.4.3; Philo, Special Laws, 1:169).

This places this Tamid Sacrifice within the exact time-frame that Yeshua was on the cross.

The lamb stays on the altar to burn all night. The next morning the priest removes the ashes and the process starts all over again.

This continuous process has a lamb, as the Tamid Sacrifice, continually burning on the altar before the Lord.

The Tamid Sacrifice also forms another sandwich in connection with the services of the Tabernacle and the two Temples. It became the bottom line pattern of the basic regular function of the services.

The singing of Psalms, the lighting of the Menorah, the burning of incense, and the prayer services are offered at the set times of the Tamid Sacrifice.

This creates the outcome structure that the rest of the services of the Tabernacle and the two Temples were built on.

To this day, the set times of Jewish prayers are said to the times of this Tamid Sacrifice. This brings us to the third sandwich – the design of Jewish prayer

Some people do not know how to pray. Some people pray to preach a sermon; but that is not the structure of the Jewish prayer.

The original Tamid Sacrifice was done by the command and authority of God. It is this authority that is recognized in the Jewish prayers.

The format is:
1) Recognize the Authority of God
2) The requests/causes being asked
3) Recognize the Authority of God

This pattern presents itself in the Lord’s Prayer, and the prayer shown in Acts 4:24 – 31.

What were the Jews in the Temple praying for when Yeshua died?
According to ancient Jewish tradition, as found in the Mishnah and Talmuds, the daily Tamid did not just deal with sacrifice; prayers also accompanied it.

Jews everywhere said these prayers while the sacrifices were being offered in the Temple.

According to these traditions, a series of blessings, commonly known as the “Eighteen Benedictions,” were being said by Jews everywhere in union with the Tamid (b. Ber. 26b; Gen. R. lxviii).

The Rabbis claim that this was taking place even during the Second Temple Period (see Babylonian Talmud, Ber.33a, Meg. 17b)

Yeshua own followers would go up to the Temple at the hours of the perpetual sacrifice to pray.

This is explicit in the book of Acts:
Now Peter and John went up to the Temple at the hour of prayer, the ninth hour (=3 p.m.) (Acts 3:1; cf. 2:15).

Ancient Jewish tradition states that the Eighteen Benedictions were the prayers during this time.

This forces a question: What were they praying for during the Tamid sacrifice and while Yeshua was dying on the Cross?

1. According to Jewish tradition, at 9 a.m. and 3 p.m., the Jews in the Temple was praying for redemption:
“Look upon our affliction and plead our cause, and redeem us speedily for your name’s sake, for you are a mighty redeemer. Blessed are you, O Lord, the redeemer of Israel.” (7th Benediction)

2. According to Jewish tradition, at 9 a.m. and 3 p.m., the Jews in the Temple was praying for the forgiveness of sins:
“Forgive us, O our Father, for we have sinned; pardon us, O our King, for we have transgressed; for you pardon and forgive. Blessed are you, O Lord, who is merciful and always ready to forgive.” (6th Benediction)

3. According to Jewish tradition, at 9 a.m. and 3 p.m., the Jews in the Temple was praying for the coming of the Messiah:
“Speedily cause the offspring of your servant David to flourish, and let him be exalted by your saving power, for we wait all day long for your salvation. Blessed are you, O Lord, who causes salvation to flourish.” (15th Benediction)

4. In fact, according to Jewish tradition, at 9 a.m. and 3 p.m., the Jews in the Temple was praying for the resurrection of the dead:
“You, O Lord, are mighty forever, you revive the dead. You have the power to save. You sustain the living with loving kindness. You revive the dead with great mercy. You support the falling, heal the sick, set free the bound and keep faith with those who sleep in the dust. 

Who resembles you, a king who puts to death and restores to life, and causes salvation to flourish? And you are certain to revive the dead. Blessed are you, O Lord, who revives the dead.” (2nd Benediction)

POINT: Ancient Jews were praying for the very things the body of Messiah believe were dispensed by Yeshua on the Cross, at the very hour he was dispensing them

One final question: Why were there two lambs for the Tamid Sacrifice?

I will give you two possibilities. You can choose “either/or” or “both/and“

1) The bottom lamb is Messiah Ben Joseph and the top lamb is Messiah Ben David
2) The bottom lamb refers to the first coming as the Suffering Servant and the top lamb refers to the second coming of our Messiah, Yeshua as the king

Where is the fundamental proof text for this understanding?

It is written in Hebrews 9:28 “In the same manner the Messiah also was offered in sacrifice once to take away the sins of many. He will appear a second time, not to deal with sin, but to save those who are waiting for him.“