"Depend on," "rely on," "rest on," and "hinge on" are all synonyms for the phrase "lie upon." These terms imply a sense of weight or importance placed on a certain factor or decision. Using a synonym can add variety and depth to your writing and can also clarify your intended meaning. For example, instead of saying "the success of the project lies upon the shoulders of the team," you could say "the success of the project depends on the efforts of the team." By using different synonyms, you can communicate your message in a more powerful and concise way.