We have seen that although the right side is always given precedence over the left, the left shoe is tied before the right shoe, because the Tefillin is tied to the left arm, showing that with regard to tying, the left is given precedence.
Seemingly, this would mean that a lefthanded individual – who wears Tefillin on his right arm – should tie his right shoe first.
In truth, however, the Halacha in this regard depends not on whether a person is lefthanded, but rather if he is "left-legged" – meaning, if his left leg is stronger than his right leg. If it is, then he should tie his right shoe first, regardless of whether he is righthanded or lefthanded. A "right-legged" person, however, ties his left shoe first, even if he is lefthanded.
If a person is placing shoes on somebody else's feet – such as an employee in a shoe store, or an aid tending to an elderly individual – the procedure depends on the person whose shoes are being put on, and not the person who is putting on the shoes for him. Thus, if, for example, the customer at a shoe store is "right-legged," then the person putting on his shoes should tie the left shoe first, even though he – the store employee – is "left-legged."
If, for whatever reason, one currently has only his left shoe available, he should wait until his right shoe is brought so he can put it on first. He should not put on his left shoe while waiting for his right shoe.