Can a lycanthrope or other shapeshifter be willingly affected by the spell True Polymorph? I know that it can be affected by regular Polymorph, but the text for the enhanced version seems to differ.
No, a Shapchanger such as a Lycanthrope can not be affected by True Polymorph; regardless of it being a willing target or not.
The text of Polymorph says an unwilling creature must make a saving throw against the spell. Shapechangers automatically succeed on the save.
This could be taken to mean that if the Shapechanger is willing, there is no save for it to automatically succeed against and it is thus affected. The text of True Polymorph differs in stating quite directly that Shapechangers are flat out unaffected by this spell, instead of automatically succeeding on the saving throw. A creature that is unaffected by a spell, willing or otherwise, is immune to its effects.