Fortunately, losing the key to your Husqvarna mower is not nearly as bad as losing the key to your car. Most importantly, you'll still be able to get to work tomorrow. And (only a little less importantly), because most riding mower keys are universal, there are more places than the dealership to find a replacement key. And if you're lucky, you won't have to wait for it to be shipped. But until you get one, you won't be able to mow your lawn. To save yourself the lost mowing time next time, order two keys just in case one gets lost again and give it to your neighbor.
Send a request via Husqvarna's customer support form (http://www.husqvarna.com/us/homeowner/support/customer-support/). Include the model and serial number of your mower and request that they ship you a replacement key. Although this method will take longer than any other (and perhaps cost more), the manufacturer is sure to have your key if all else fails.
Call your local dealership. If you're lucky, they may have a key on hand that you can drive over and pick up for a small fee. If they say they have to order it however, contact the manufacturer first to see if you can have the key at a cheaper price.
Find a riding mower repair shop in your area. They may have a Husqvarna mower key on hand.
Buy a universal ignition key. Universal ignition keys, like the one listed in the resources section, start a wide variety of riding mowers including Husqvarna. But before you purchase one, make sure that your riding mower's model number is included in the list of compatible mowers.