You should not use JavaScript's falsy comparisons if false, 0, NaN, or the empty string are valid values in your localStorage.
Instead you should check if the item is equal to null or is equal to undefined:
var a = localStorage.getItem('foo');
if (a === null || a === undefined) {
    // Function
}
Note that the triple equals (===) operator compares exactly, without type coercion. Using double equals (==) operator a special set of rules are applied to covert similar values but of different types. One of the most useful of these is that null == undefined, allowing simplification the above code:
var a = localStorage.getItem('foo');
if (a != null) {
    // Function
}
If a is null or undefined the code inside will not run.