Other lords fall, the LORD does not
The previous verse in Isaiah 26 provides the antecedent for verse 14:
13 O Lord [Yahweh] our God, other lords [adonim] beside thee have had
dominion over us: but by thee only will we make mention of thy name.
14 They [the adonim] are dead, they [the adonim] shall not live; they
[the adonim] are deceased, they [the adonim] shall not rise: therefore
hast thou visited and destroyed them [the adonim], and made all their
[the adonim] memory to perish.
The LORD (Yahweh) will be praised and have dominion; the lords (adonim) will not.
The distinction is more apparent if adonim (אֲדֹנִ֖ים) is rendered "masters" instead of "lords" (which creates an unnecessary redundancy in English).
Who are the adonim?
The “other lords” are the conquerors and oppressors by whom Israel had
been enslaved; possibly also, the false gods with whom those
conquerors identified themselves.
Those tyrants are destroyed, they shall never live or rise again to
molest us. He probably refers to the miraculous destruction of
Sennacherib’s army before Jerusalem
Isaiah's people have been delivered from the oppression of other nations (e.g. 2 Kings 19:34-35); they have also cast out false gods that had been worshipped in the land in the past (e.g. 2 Kings 18:4-6)
These false gods have no life and never will. These oppressive nations have been broken and will rise no more.
Who will rise?
Empires & false gods may remain lifeless, but Isaiah is quite clear a few verses later that men will not:
Thy dead men shall live, together with my dead body shall they arise.
Awake and sing, ye that dwell in dust: for thy dew is as the dew of
herbs, and the earth shall cast out the dead. (Isaiah 26:19)
The Interrogative Psalm
In Psalm 88:10-12 six questions are asked--note that each of them is a question asked by a man contemplating death, not a statement or an answer.
This says nothing about the consciousness or unconsciousness of the dead, but does perhaps suggest the futility of procrastinating turning to the Lord. It asks a question which is graciously answered elsewhere--yes indeed the dead will rise.
This is not dissimilar to the pondering of Job:
If a man die, shall he live again? (Job 14:14)
If the question were never answered, this would be a much more depressing book. Fortunately, 5 chapters later:
25 For I know that my redeemer liveth, and that he shall stand at the
latter day upon the earth:
26 And though after my skin worms destroy this body, yet in my flesh
shall I see God (Job 19:25-26)
Contradiction question: Isaiah 14:9 suggests that Rephaim are raised, whereas Psalm 88:10 & Isaiah 26:14 affirm that Rephaim will not rise. Is this a contradiction?
No, the Psalm is asking a melancholy question; the Isaiah passage refers to different entities (fallen empires will not rise; the individual people from them will rise)
On the resurrection of the dead: if Psalm 88:10 & Isaiah 26:14 affirm that Rephaim will not rise, how can this be reconciled with the New Testament promise of the resurrection of the dead on Judgement Day? Were Isaiah & David ignorant of the resurrection? Why would they say that Rephaim will not rise?
There is no contradiction--it is quite common for a conqueror in war to describe the enemy by saying "they will never rise again [to attack us]". When a warring nation demands unconditional surrender it is for just this purpose--to make sure the opponent never again has the resources to conquer. The Psalm asks a question that is graciously answered elsewhere--in both the OT & NT.
Isaiah & David were not ignorant of the resurrection (e.g. see Isaiah 26:19, Psalm 16:10).