Icelandair does offer a business class on its international flights called the "Saga Class". Travelers can get several features for passengers traveling in this class, such as spacious, lie-flat seats with delicious meal options and complimentary drinks. The Icelandair Business Class seats are not fully lie-flat, but they still have comfortable seating during the journey. If you need assistance with business class flights, you can contact Icelandair customer service or read the blog by Airlines Group Travel.