I wonder if any hit to Dame's reputation lasts longer than a few weeks or months (or even longer than a day after the eventual trade happens). I'm trying to think of examples of other stars who made public trade demands to specific teams, and other than Anthony Davis, I'm drawing a blank. AD's reputation has certainly tanked since that trade demand, but that's mostly because of his on court deficiencies (and inability to actually stay on the court).
I think his reputation will be fine, but I think the Blazers' reputation, if they hold out, will be totally fine too.
We just went through this last summer with Durant:
1. KD requests a trade with 4 years left on deal, to a hand-picked list of teams
2. Nets accomodate, but don't like the offers
3. KD tries to up the pressure ("fire Marks and Nash!")
4. Nets don't give in
5. KD reports to camp, plays well for the Nets
6. Nets eventually trade him for a really nice haul
So far, this is identical to the Lillard scenario, except that Lillard has only one team on his list, and its assets are crappy. The Blazers saw this play out, and saw that the Nets did fine reputationally calling the bluff, and came out with more assets. I doubt they fold this early for Miami's pupu platter.