To give a definitive answer to this question I would want to base it on some commentaries on the meaning of the Vigil. However, I have not seen any commentaries on the Vigil that have been translated into English that discuss the significance of singing this hymn at the point in the service that it is sung. I would think that there probably are such commentaries in Greek or Russian. Perhaps someone who is familiar with them will fill me in on what they say in response to posting this question, and if they do, I will post an update. There may also be something that is in English which I have simply not read yet. What I will do is point out a few facts about this hymn, and then give you my thoughts on why it may be that it is sung when it is, but I could be off the mark on it, and so don't take it as a final answer.
The way "Holy is the Lord, our God" is sung at Sunday Matins is the Deacon intones it is a way similar to a prokimenon, and the Choir repeated sings the verse, as follows:
Deacon: Holy is the Lord our God.
Choir: Holy is the Lord our God.
Deacon: For holy is the Lord our God.
Choir: Holy is the Lord our God.
Deacon: Above all peoples is our God.
Choir: Holy is the Lord our God.
"Holy is the Lord, our God" is only sung during Sunday Matins, with two exceptions: It is sung at the Matins of Lazarus Saturday, and it is also sung on Holy Saturday. So there is something about the significance of Sunday that calls for this to be sung, and so the obvious link would be with the Resurrection. And in fact, both Lazarus Saturday and Holy Saturday are services that anticipate the celebration of the Resurrection of Christ, and both services have a number of elements that are usually associated with the Sunday Services -- for example, on Lazarus Saturday, we sing "Having beheld the Resurrection," and on Holy Saturday we sing the Evlogitaria of the Resurrection. Another instance in which it is sung is at the Matins of Palm Sunday, when it is sung -- not prior to the Exapostilarion, as on Sundays -- but as the Exapostilarion. And while Palm Sunday is of course a Sunday, we do not sing any of the usual hymns of the resurrection on Palm Sunday.
So what is an Exapostilarion? According to the Festal Menaion, an exapostilarion takes its name from the Greek exapostello, "dismiss"), and so it is a hymn that we are dismissed with at Matins. And so has some special significance and is given a place of prominence during that service. The fact that this hymn functions as an exapostilarion on Palm Sunday (and also on Holy Saturday) probably indicates that when it is used just before the exapostilarion on Lazarus Saturday, and on normal Sunday services, that it is sort of a exta-exapostilarion. I also think that the fact it is the exapostilarion of Palm Sunday indicates that it is not just pointing to the Resurrection, but also to Christ's death on the Cross.
This is further indicated, in my opinion, by the Psalm from whence these verses are taken. Psalm 98 in the Septuagint (Psalm 99 in the KJV and most English versions of the Bible) focuses on the Ark of the Covenant, and the Mercy Seat, which I talk about in a sermon that you can listen to by clicking here. As I discuss in that sermon, this Psalm has verses that are used on the feast of the Exaltation of the Holy Cross, and so its use on that feast connect it with the Cross of Christ, and St. Gregory Palamas likewise associates the Ark of the Covenant and the Mercy Seat with the Cross, as is mentioned in that sermon.
And so it seems to me that this hymn is sung to remind us of the awesome mystery of Christ's death and resurrection, and to emphasize the sacredness of that mystery which we celebrate especially as we enter into Passion week on Palm Sunday, when we anticipate the celebration of Pascha on Lazarus Saturday and Holy Saturday, and when we celebrate Pascha each Sunday throughout the rest of the year.
