The question comes up as to why the entire psalter is not found in the LSB. (The entirety isn't found in the LW or the TLH, either).
The quick answer is that some of the Psalms are not used in the propers for any days, and so they aren't "needed," in that sense of the word.
What I would very much like to see is a fuller exploration of the Psalms in the praying life of the church. When they aren't in a worship book, it's a guarantee that those Psalms not printed won't be used. Most of us are lazy. If the Psalm isn't printed, we won't go to the bother of working it into a prayer life.
I'm troubled that those not appointed (and not printed) tend to be the more troublesome of the Psalms, especially the imprecatories. Psalm 83 is a good example.
1 Keep not thou silence, O God: hold not thy peace, and be not still, O God.
2 For, lo, thine enemies make a tumult: and they that hate thee have lifted up the head.
3 They have taken crafty counsel against thy people, and consulted against thy hidden ones.
4 They have said, Come, and let us cut them off from being a nation; that the name of Israel may be no more in remembrance.
5 For they have consulted together with one consent: they are confederate against thee:
6 The tabernacles of Edom, and the Ishmaelites; of Moab, and the Hagarenes;
7 Gebal, and Ammon, and Amalek; the Philistines with the inhabitants of Tyre;
8 Assur also is joined with them: they have holpen the children of Lot. Selah.
9 Do unto them as unto the Midianites; as to Sisera, as to Jabin, at the brook of Kison:
10 Which perished at Endor: they became as dung for the earth.
11 Make their nobles like Oreb, and like Zeeb: yea, all their princes as Zebah, and as Zalmunna:
12 Who said, Let us take to ourselves the houses of God in possession.
13 O my God, make them like a wheel; as the stubble before the wind.
14 As the fire burneth a wood, and as the flame setteth the mountains on fire;
15 So persecute them with thy tempest, and make them afraid with thy storm.
16 Fill their faces with shame; that they may seek thy name, O LORD.
17 Let them be confounded and troubled for ever; yea, let them be put to shame, and perish:
18 That men may know that thou, whose name alone is JEHOVAH, art the most high over all the earth.
Most of us have trouble reading that -- much less praying it -- without gulping. But this is one of those hard passages of scripture that we need to deal with, wrestle with, "understand" (in the old sense of standing under it, of learning from it) it. If we are content to ignore portions of God's word, our understanding of God's revelation will be truncated. What's more, our ignoring the hard passages often indicates an insufficient appreciation of the reality of evil, and a mental inability of dealing with evil, especially with regard to our prayers.
God is love, and that God Who is love is likewise completely realistic about sin and the horror it has brought upon us. The hard Psalms tell us about that. We are the worse off for ignoring what they tell our Father.