In Luke 18:8, does the Geek word translated “quickly” mean “suddenly” in this instance? We know that in our lives on planet earth the Lord does not always quickly protect those who are suffering injustice. Definitely, he will on the day of his visitation correct injustices and he will rule with perfect justice during the millennium. But it seems that many people, while living on planet earth, undergo major and continuous injustice even though they pray frequently for God to relieve the injustice.
I do not have sufficient knowledge of the Greek to understand how verse eight is true if I understand it to be translated “quickly.“
The word is τάχος Strong 5034 which Thayer (see the link for Strong) renders as 'quickness' or 'speed'.
So in the construction used in verse 8, ἐν τάχει, Thayer tells us that the meaning is quickly or shortly (as in Acts 12:7; Acts 22:18; Romans 16:20) or it may mean speedily or soon (as in Luke 18:8; 1 Timothy 3:14 ; Revelation 1:1; Revelation 22:6).
Thus the execution of judgment is speedy, when the time comes to execute that judgment.  However the verse is not stating that there will not be a delay, ere the time of execution will occur.
It is only stating the rapidity of executed judgment, when the time for judgment to be appropriate arrives.
We know, from many other scriptures (such as the entire book of Job, or the forty years that Moses spent in  Midian, or the hundreds of years during which God waited before flooding the whole earth) that there may well be reasons, in God's purposes, for time to pass, until it is the right time for a reconciliation to occur.
But once that period of time has elapsed, the judgment falls swiftly, as exampled in the days of the Flood during Noah's lifetime, or as exampled in the judgment upon Sodom and the cities of the plain in the days of Abraham and Lot.