Luxuriously is the adverb: it tells you how something is done or how someone lives — in a very expensive, beautiful, and comfortable way. You might stretch luxuriously on a sofa, live luxuriously, or be luxuriously comfortable. The word paints the manner, not the thing itself.

It is a little dressy, like the adjective it comes from. In simple talk, people often just say in comfort or like a king, or they skip the adverb and use luxurious on the noun instead. Though actually, luxuriously is still the right choice when you need to modify a verb: “She stretched luxuriously” is neat; “She stretched luxurious” is not English. Use it when the way someone rests, travels, or is treated is the point.