What does “for Jesus’ sake” mean?

I often read in Christian publications and in our own WELS literature the phrase "for Jesus' sake." This often appears at the end of written prayers and in the prayers said at the altar in my home church. I really bristle at this. For Jesus' sake? Really? He is holy and gave us eternal life through His holy blood. Jesus doesn't need us to pray for him. It is we poor sinners who need prayers of intercession. As a life-long WELS member, I finally have to ask, what does this phrase mean, as I obviously am missing the meaning?

Your question illustrates how words can have multiple meanings.  “Sake” can mean “for the benefit of” or “on account of.”

The expression “for Jesus’ sake” at the end of prayers does not intend to say that we are praying for (“for the benefit of”) Jesus.  “For Jesus’ sake” means that we are coming to God in prayer, not pleading our own merits, but (“on account of”) Jesus’ merits.

Jesus said, “I am the way and the truth and the life.  No one comes to the Father except through me” (John 14:6).  When we end our prayers with “for Jesus’ sake,” we are acknowledging that Jesus is the one who has bridged the gap between a holy God and sinners.  “For Jesus’ sake” has the idea of asking that our prayers be heard and answered, not because of who we are but because of who Jesus is.  And of course whether or not we use that expression, that thought is foundational to all our prayers.

So, keep presenting your “requests, prayers and intercession” (1 Timothy 2:1) to God.  God will hear and answer your prayers for Jesus’ sake, because he has “reconciled us to himself through Christ” (2 Corinthians 5:18).