1. Because she was the richest movie star in the business, she had a magnificent house, servants, cars and clothes. She was living in the lap of luxury.
2. If this business deal succeeds, we’ll never have to worry about money again. We’ll be living in the lap of luxury.

The lap of luxury means a very comfortable life because one is rich, whereas the life of Riley is an easygoing life because one doesn’t have to work or isn’t working. Someone who is poor can lead the life of Riley if he or she doesn’t mind being poor.