Is luxury a proper noun

No, the noun luxury is a common noun, a Word for any luxury of any kind.

A proper noun is the name of a person, place, thing, or a title; for example:

• Luxury Street, Moreno Valley, CA
• Luxury Circle, Jackson, NJ
• Luxury Drive, Concord, CA
• Luxury Row (designer shops), Honolulu, HI
• "Luxury Liner", 1948 movie starring Jane Powell
• "Deluxe: How Luxury Lost Its Lustre" by Dana Thomas