Who lets you download a map update? I didn't think Lexus provide any free updates, unlike Toyota who give you three years. Map updates contain firmware, so if you can get a map update then you will be updated. Firmware updates however come out more frequently if there are bugs that need to be fixed, so rather than wait for a new map you can get a firmware update.
You don't have to pay, your vehicle is under warranty. Tell them you have issues with your nav and they will apply the latest firmware FOC. Once it is out of warranty the dealer will charge you labour for them to update it.