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An arahant or Buddha would never lie, including lying about lying.
However, a Sammasambuddha (a complete Buddha, with the extraordinary ability to teach the masses) may tell the truth about telling different types of truth, that may appear to conflict with each other, but they don't, in actual fact.
A good example is the noble right view vs. the right view with effluents.
"And what is right view? Right view, I tell you, is of two sorts: There is right view with effluents, siding with merit, resulting in acquisitions [of becoming]; there is right view that is noble, without effluents, transcendent, a factor of the path.
"And what is the right view with effluents, siding with merit, resulting in acquisitions? 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are contemplatives & brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is the right view with effluents, siding with merit, resulting in acquisitions.
"And what is the right view that is noble, without effluents, transcendent, a factor of the path? The discernment, the faculty of discernment, the strength of discernment, analysis of qualities as a factor for awakening, the path factor of right view in one developing the noble path whose mind is noble, whose mind is without effluents, who is fully possessed of the noble path. This is the right view that is noble, without effluents, transcendent, a factor of the path.
MN 117