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

Solution 1:

"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.