We all know that lying is not telling the truth. But do you think it's possible to lie without saying a word

In a sense, yes.  One can create the effect of a lie by withholding truth.  For example, if at work Rob is accused of leaving a mess that I know Jon had made if I say nothing in Rob's behalf I allow Rob to be accused wrongly.  The effect is the same as if I lied and said, "Rob made this mess."

Absolutely. That's known as "a lie by omission", where one deliberately allows deception by NOT speaking up and correcting a misunderstanding.