So the illustration shows only one entrance to the courts. The courts are divided in the outer courts, the Holy place and the most holy place (where the arc of the covenant was). First the priest needed to sacrifice a selected/set apart animal for sacrifice and use the blood to be able to reconcile with God. Second is the washing of the hand & feet.
!Remember in every book of the Bible we find Jesus' presence; what do I mean? There is just one way to get to the Father, in the OT reconciliation was through sacrifice of animals, in the NT Jesus is the only way to reconcile with God the Father; the price paid was the blood of Jesus, the Lamb of God. The Washing of the feet does happened in the NT. Remember what did Jesus do to His disciples? He washed their feet, to be cleansed and to walk in holiness.
During this time of Lent, remember all these things and keep them in your heart. Delight yourself in the word of God.

Exodus 30:17-21 Bronze basin/Brazen Laver

Brazen Laver

17 The Lord said to Moses,18 "You shall also make a basin of bronze, with its stand of bronze, for washing. You shall put it between the tent of meeting and the altar, and you shall put water in it,19 with which Aaron and his sons shall wash their hands and their feet.20 When they go into the tent of meeting, or when they come near the altar to minister, to burn a food offering to the Lord, they shall wash with water, so that they may not die.21 They shall wash their hands and their feet, so that they may not die. It shall be a statute forever to them, even to him and to his offspring throughout their generations."