This is a complex question. During the opening section of the novel, Nick discusses his humility while also describing his own ambitions and arrogance. We might resonably ask if he is discussing "honesty" in the same ironic manner.
There is little evidence to suggest that Nick is lying when he says he is honest, but there is adequate evidence to suggest that we should see more than one meaning to his boast - and this is, importantly, a boast. In the opening chapter, Nick states "snobbishly" that he is possessed of real virtue - the virtues of forbearance and humilty in particular.
We should also consider the larger irony of the opening section when assessing Nick's later claims. Nick states that the "intimate revelations of young men" are "usually plagiaristic and marred by obvious suppressions", yet he is essentially offering a preamble to an intimate revelation of his own. This is no coincidence. This notion is weighted with irony.
The resulting complexity regarding Nick's candor can be applied also to Nick's claim of honesty. Just as Nick derides his own ambition to become "that most limited of all specialists, the 'well-rounded man'", we might wonder if his claims of honesty are undermined by his affiliations with liars, his tendencies to obfuscate and "suppress", and reflective of a certain self-serving self-deceit.
Given the complexity of Nick's self-presentation in the opening section, all of his later claims are suspect to some degree. When we also consider the rumors of his relationship with a college sweetheart that are discussed as false in the first chapter, we might add even more suspicion to his claims of honesty as they appear in the immediate aftermath of a visit with his new girlfriend, Jordan.
Nick brings up that old relationship just before saying he "suspects himself" of honesty.
With so many layers to read through, we cannot simply say that Nick is lying when he says he is honest. Nor can we assume he is telling a simple truth.
As Nick's claim to honesty is actually presented as a suspicion, we might ask if this is a moment where Nick decieves himself willfully as Gatsby, Daisy, and others do elsewhere in the novel, and suspects that this is exactly what he is doing.