it's incorrect to say competitive strategy- because LVMH is not a business. LVMH doesnt compete with anyone because it is a conglomerate of decentralized brands. Each brand has its own DNA/story/value proposition and its own competitors and unique business strategies.
Having said that, LVMH's 'corporate' strategy is to hold a portfolio of the most cherished, coveted luxury brands and add value through its specialized resources - sourcing, its supply chain management, brand management and talent.