How can "to have no illusions that something will happen" mean to be convinced/aware that something will happen?

"The U.S basketball team have no illusions that they can beat Lithuania" means that U.S. team is rightly convinced that it cannot beat Lithuania. This seems like it must be a typographical error, because, yes, the U.S. team (i.e., a team of major college and/or professional players, as in the Olympics) would certainly be favored over Lithuania. Be that as it may, the opposite would be "The U.S. team has the illusion that it can beat Lithuania," meaning that the U.S. team believes it can win, but that the speaker believes this is an impossibility. In both cases, the speaker is convinced the U.S. cannot win--perhaps the speaker is a Lithuanian? In your sentence, the U.S. agrees with this assessment--it cannot win; in the opposite, the U.S. disagrees with the idea that it cannot win, but the speaker remains convinced that it cannot.

I reckon the phrase "have no illusions that" should be interpreted as "have no doubt that (=believe that)". As an example of this usage, I wll cite a quotation from "The Day of the Jackal" by Frederick Forsyth below.

A lean and fanatical colonel in Rome had devised a plan that could still bring the whole edifice tumbling down by organising the death of a single man. Some countries have institutions of sufficient stability to survive the death of a president or the abdication of a king, as Britain had shown twenty-eight years earlier and America would show before the year was out. But Roger Frey was well enough aware of the state of the institutions of France in 1963 to have no illusions that the death of his President could only be the prologue to putsch and civil war.