The reason why there is no remembrance of the Lord in the grave, is because there is no conscious thought. In fact, in Psalm 88, which also speaks of death and the grave, it is referred to as "the land of forgetfulness", as we see here :
"Shall thy wonders be known in the dark? and thy righteousness in the land of forgetfulness?"
Psalms 88:12, KJV
The writer of Ecclesiastes also tells us :
If there is no knowledge or wisdom in the grave, it can only be because there is no conscious thought. While this is the fate of our physical bodies following death, what about our spirits? For the saved Christian, the scenario is very different. As the Apostle Paul tells us :
"We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord."
2 Corinthians 5:8, KJV
"But if I live in the flesh, this is the fruit of my labour: yet what I shall choose I wot not. For I am in a strait betwixt two, having a desire to depart, and to be with Christ; which is far better: Nevertheless to abide in the flesh is more needful for you."
Philippians 1:22-24, KJV