You must make Foo::comparator static or wrap it in a std::mem_fun class object. This is because lower_bounds() expects the comparer to be a class of object that has a call operator, like a function pointer or a functor object. Also, if you are using C++11 or later, you can also do as dwcanillas suggests and use a lambda function. C++11 also has std::bind too.
Examples:
// Binding:
std::lower_bounds(first, last, value, std::bind(&Foo::comparitor, this, _1, _2));
// Lambda:
std::lower_bounds(first, last, value, [](const Bar & first, const Bar & second) { return ...; });