According to The Prince, would a Machiavellian leader be likely to lie to his subjects in order to avoid scandal or opposition?
A Machiavellian leader should lie to his subjects if it is necessary. A leader has to always act in ways that will make his people respect him, even if this means that he has to break his word.
The difficulty is that a ruler needs to have a reputation for being honest even as he lies and deceives. He has to manage to project an aura of honesty no matter what he actually does. What Machiavelli is saying, then, is that the ruler has to be a good actor. He has to be able to come across as trustworthy even when he is lying.
If circumstances change and a leader's promise looks like it will get him in trouble, he will have to go back on his word and then lie about what happened. For example, Mitt Romney promises that he will declare China to be a currency manipulator on his first day in the White House. If he gets elected, he may find that this is a bad idea. In that case, he may need to go back on his word but then claim that he is doing it because China has shown that they are changing their ways.
So, yes, a leader would and should be likely to break his word in order to avoid serious opposition from his subjects.