Redcloak seems to be confident that he can deal with Xykon at his convenience. Holding a lich's phylactery is one heck of an advantage.
He could have used his brother's attack to take out Xykon.
He could have used the duel with Dorukan to initiate an attack on Xykon.
He could have used Roy's destruction of Xykon to eliminate Xykon with no risk at all.
He could have helped the ghost martyrs kill Xykon, or he could have simply stopped Miko from destroying the gate so the GMs could finish the job.
By these skipped opportunities I conclude that Redcloak chooses to work with Xykon. He does not want any option but the one he chose before he ever innitiated the attack on Lyrian's Gate.
A plan unchanged, that he refuses to modify after multiple failures: fallacy.
A set of goals the plan is supposed to achieve, which have been demonstrated to be achievable by other means, still being pursued by a plan which has failed four times. Fallacy.
A key person, required to fulfill the plan, whose actions to date indicate that he is actually opposed to the goals of the plan, being retained after multiple opportunities to remove and replace him with someone more malleable: big fallacy.
Both the Sunk Cost and the Fallacy are in play here, and both are repeatedly and obviously made known to Redcloak and rejected because The Plan Must Succeed To Prove I Was Right.
(Not for the betterment of goblinkind, his stated goal.)