There are several synonyms for the phrase "lie one's way out of," which refers to someone using falsehoods to escape a situation or avoid responsibility. One similar phrase is "fib one's way out of," which also involves telling small lies to get out of trouble. Another synonym is "dissimulate," which means to conceal one's true feelings or intentions through deception. "Prevaricate" is another option, which means to avoid telling the truth or to be deliberately vague. Finally, "fabricate" can also be used, which involves creating a story from scratch to avoid the truth or reality of a situation. Regardless of the exact words used, these synonyms all describe a similar pattern of deception and dishonesty.