Yes, we don't know what they did there. They went to the East, and there they entered total obscurity.
They may have, as Tolkien speculates, played an important role in the restraint of Rhun (i.e. by convincing a part of the inhabitants of the East not to follow Sauron) and certainly their purpose was to do this. However, perhaps they did not succeed in this. Obviously they failed to sway the governorship of Rhun, and that it probably what really counted. The kings of Rhun, or even pressure from other people, could well have enforced those unwilling to fight to go anyway. It is also more than likely that hearing of these two upstarts apparently recruiting for the West in their kingdom, they or angry followers had them killed.
The notion, also raised by Tolkien, that they in fact fell into evil themselves in the East and actually assisted the rulers may also be viable. The fact is that they Ithryn Luin are so obscure that we don't really know anything about them, and that Tolkien's comments on them are varied and contradictory -- a commentry and a speculation themselves. They highlight possible explanations but don't define anything.
It is interesting to note a couple of other things. Firstly, that Easterlings could be willing to fight for the West, as some (Bor the Faithful and his sons) did not betray the Elves in the Nirnaeth. Secondly, that we do not see any information on what was happening with the Blue Wizards from Saruman; and also that they were not there at the sailing into the West of the Last Ship (although they may have taken another). Had they been alive and victorious, as Gandalf was, it would perhaps be expected that they would have been there at that sailing back into the West.
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