What does "lie with" mean?

Rule utilitarianism has the great practical benefit that it makes it unnecessary to perform a complicated calculation every time you are faced with having to make a moral decision. However, in a situation in which you know that greater happiness will result from breaking a promise than from keeping it, and, given that your basic moral sympathies lie with a utilitarian outlook, it seems perverse to stick to the rule rather than to treat the individual case on its merits.

What does "lie with" mean?