Cisco Limited Lifetime Warranty is "black hole" in that the Entitlements Team would "feign" ignorance. I've successfully RMA-ed a lot of switches and APs using the LLW/E-LLW and I've always go into an argument (sometimes with the same person) about what LLW/E-LLW means.
No, the appliance doesn't need to have a valid Service Contract to invoke LLW/E-LLW. The only thing the appliance need to have is the serial number MUST BE attached to your CCO login.