How long after eating does someone have to wait before taking levothyroxine. In other words, what's the definition of an empty stomach?

No soy no iron. Although the packaging for levothyroxine says to take it on an empty stomach for many people its not possible to do that and take it consistently each day. As long as you take it at a consistent time and don't take it with soy or with iron which will interfere with its absorption it is fine to take it with breakfast or before bed without being strictly fasting. Just get labs checked after change.
One hour. Generally one hour, but it's not really necessary if you take the pills consistently under the same circumstances each day and you lab tests show normal levels. Take only brand name replacement and do not take within 2 hours (before or after) iron, calcium or vitamins.