History, properly defined, is provable. Either something happened or it did not, and that can be established by the evidence.
It is not necessary to believe that Jesus (or God) lied because, whenever there is a discrepancy between the New Testament and historical fact, there is another, straight-forward option to consider. When Jesus is reported as saying or doing something, it can simply be that he was misreported, or even that the passage was a literary invention. This appears to occur often right throughout the Bible.
Our church and the Bible never tell us that Jesus has lied, but since lying is a sin, it is most likely he never did.
Historical events are events that have be proven true, are not lies. There are many types of history.
This question turns upon how we "prove" that any historical event occurred and that is worth some thought. (It is equivalent to asking how we know that a particular historical event really happened or is "true").
First, it is not possible to prove the event as we would prove a mathematical theorem. Second, it is not possible to prove the event as we would prove a predicted result in chemistry by repeating the experiment - history is a one-time event, so to speak. That leaves us with the old "proof beyond a reasonable doubt" of the law court that depends upon a variety of factors (such as testimony of eyewitnesses, corroborating circumstances, and supporting facts) but that is not "absolute" proof. Therefore, there is always some uncertainty to any - any - historical claim.