L does not earn mileage on CX but does on AA/BA/QF. You can check on aa.com to see what it earns on the airlines involved in your LONEx fare routing. Minimum level for lounge access is Platinum. Some airports have free or paid showers (e.g. LHR, SYD) and most have paid lounges that you can use (these vary from quite good to abysmal, and cost also varies greatly). The LONEx is a deeply discounted economy fare and most airlines will treat you like that (no benefits or entitlements). That's why most discussion on this forum is about the DONEx and AONEx fares.