In a small saucepan, whisk together the soy sauce, mirin, sugar and sake; bring to a boil. Simmer over medium heat, stirring constantly, until the mixture has reduced to about ¼ cup (about 12 minutes). It will be rather syrupy. Let cool.
When cooled, whisk in the mayonnaise and lime juice, and season with salt..
Keep refrigerated until ready to use with salmon. If it thickens up too much, just heat it a bit to soften it. Drizzle over salmon and marinate for about an hour before grilling or baking. You can brush the sauce on while cooking if you'd like to.