Can I use Polaris lounge on arrival if connecting flight is economy?

Im flying from Europe to New York on Business. Then New York to LAX economy. Can I use the LAX polaris lounge on arrival? Also in general, when using a lounge on arrival what happens to checked luggage? Does it just sit on the coursel at risk of being taken? Or will it be collected by UA staff if it sits at the carousel for too long?

Thank you!