Where is the lock for a std::atomic?

If a data structure has multiple elements in it, the atomic version of it cannot (always) be lock-free. I was told that this is true for larger types because the CPU can not atomically change the data without using some sort of lock.

for example:

#include <iostream>
#include <atomic>

struct foo {
    double a;
    double b;
};

std::atomic<foo> var;

int main()
{
    std::cout << var.is_lock_free() << std::endl;
    std::cout << sizeof(foo) << std::endl;
    std::cout << sizeof(var) << std::endl;
}

the output (Linux/gcc) is:

0
16
16

Since the atomic and foo are the same size, I don't think a lock is stored in the atomic.

My question is:
If an atomic variable uses a lock, where is it stored and what does that mean for multiple instances of that variable ?