You ask for a word where:
the bad lie... [is] a hint to avoid further confrontation/questioning
Not a single word but, otherwise, white lie seems to meet your needs:
COBUILD Advanced English Dictionary:
If you refer to an untrue statement as a white lie, you mean that it
is made to avoid hurting someone's feelings or to avoid trouble, and
not for an evil purpose.
a minor or unimportant lie, esp one uttered in the interests of tact
a lie concerning a trivial matter, often one told to spare someone's
A white lie might be to avoid loss of face for either party or for both. Feigning a prior engagement to avoid openly refusing an invitation would be a white lie, as would telling someone that their hideous new dress was nice. Responding to an inquiry about work or health with a very general, short, closed, positive answer could be a white lie to avoid an awkward truth or a subject one would rather not discuss.
Wikipedia expands on their positive aspects, saying:
White lies are minor lies which could be considered harmless, or even beneficial, in the long term. White lies are also considered to be used for greater good (pro-social behavior). White lies are often used to shield someone from a hurtful or emotionally damaging truth, especially when not knowing the truth is completely harmless.
By this view, a white lie might, at times, be a very trivial form of the noble lie.
There are others views, of course. A Google Books search for "white lie" led me to this gem:
“A white lie!” she responded, “what is a white lie?”
“Don't you know?” asked Katie.
“No, nor you either.”
“But I do,” said Katie.
“Well, now, what is it?”
“Why," said Katie — “why, a white lie—a white lie—is is—a black lie with
a white dress on.”
The Ladies' Repository, Volume 17 (1857), page 62