Does the term "white lie" have racist connotations?

As with any question of political correctness, the answer depends on the audience:

There is a claim (presumably ascribed to by Sue) that the English language is liberally infested with terminology that reinforces unconscious racial biases, chiefly revolving around the "white = good, black = bad" paradigm. This claim is both common and well-received in progressive academic circles and other subgroups with an interest in raising consciousness around racial issues. When communicating in or with such a group, you would be expected to police your own language for inherent biases.

Outside of such groups, such terms are unlikely to cause offense, and can be used at your own discretion --you can decide for yourself whether your use of them is likely to reinforce bias in yourself or others (and whether apt alternate terms do exist).

Conclusion:

White in "white lie" is a reference to the perceived moral purity of the lie, an act normally considered immoral. It is not a reference to a race.

Sources

According to etymonline.com, white as an adjective is from

Old English hwit [meaning] "bright, radiant; clear, fair"

According to the same source

Meaning "morally pure" was in Old English.

A white lie is defined as in OED as

A harmless or trivial lie, especially one told to avoid hurting someone’s feelings.

It is clear from the definition that the modifier "white" is a description of the motive or impact of the lie, and not its provenance.

The meaning "characteristic of or pertaining to white people" is from 1852, American English, while the phrase "white lie" itself predates that meaning, being found as early as 1741. (etymonline)

Edit (moved this point up from the comments): This is responsive to the question in that there are no objective grounds to associate the term with a particular race.