It’s my understanding that the so-called Last Rites include the Sacraments of Confession, the Anointing of the Sick, and the Eucharist.
James wrote about the Sacraments of the Anointing of the Sick and Confession, saying:
Is any among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord; and the prayer of faith will save the sick man, and the Lord will raise him up; and if he has committed sins, he will be forgiven. Therefore confess your sins to one another, and pray for one another, that you may be healed. (James 5:14-16)
Jesus spoke about the Sacrament of the Eucharist, saying:
Truly, truly, I say to you, unless you eat the flesh of the Son of man and drink his blood, you have no life in you; he who eats my flesh and drinks my blood has eternal life, and I will raise him up at the last day. (John 6:53-54)
Although the Sacraments are not absolutely necessary since God, who gives grace through them, can also give grace apart from them, they are *ordinarily necessary *because Jesus Christ gave the Sacraments as gifts to his Church to assist us in our weakness and as a protection against presumption. Whenever we repent of our sins with a contrition motivated by love of God (so-called perfect contrition) (Luke 7:47; 1 Peter 4:8), God will certainly forgive our sins and justify us. However, if our contrition is motivated for a lesser reason (so-called imperfect contrition), there is no guarantee God will forgive us. So, if the Sacraments are available to us, we ought to make use of them because their effects are certain, even when our contrition is imperfect. Better to receive the Sacraments even though we may have perfect contrition and so be saved than to presume our contrition is perfect when it is not and neglect the Sacraments and end up damned.
For a Christian not to avail himself of God’s gift of those Sacraments and the other Sacraments, including the fruit of the Sacrament of Holy Orders, namely, God’s gift of “pastors and teachers” (bishops), given so that we might not be “tossed to and fro and carried about with every wind of doctrine, by the cunning of men, by their craftiness in deceitful wiles” (Ephesians 4:11,14), makes even less sense than for a Christian not to avail himself of the inspired writings of the New Testament, which admittedly “the ignorant and unstable twist to their own destruction.” (2 Peter 3:16)