I know that your store may be different, but in my friend's store, which is gigantic and insane, that hour is to really prepare for the day and assist guests. There's always something to be done, really. My advice is to take a deep breath, enjoy the small break in anarchy, and spend time giving great guest service and making sure everything's in order. Asking the LOD for something to do will usually just lead to busy work or whatever else to have you doing something.
The best advice my buddy ever got for Hardlines is to always find a project to take on before going ask for something to do. Chances are that you'll easily find something small to do, get to choose what you're spending your time on, appear to be self-motivated, and if there's something else they'd rather you do, they'll tell you. Don't do anything too crazy or waste time on something you know isn't worthwhile, but if you know that the rugs are always half-assed or the zone always misses a spot, no one will fault you for going tackle that if there really is nothing to do. A terrible closing shift is usually the result of things building up for days or being overlooked all day. Think about what sucks to tackle late when you close and start taking a chunk out of it early so that touch ups throughout the day keep it nice. That way, closing requires less effort to get it sparkling, and the opening TMs have less make up work to do and can get ahead of things, too.
The one lesson my friend picked up quick is that things snowball quick to the point of being in a state of perpetual recovery, and when things actually "reset" and start fresh, days are much more pleasant for everyone. So basically just give great customer service and find little projects until someone gives you one. If you want to be given a task, by all means go ask the LOD, but chances are that they're aware how slow it is and will give you something less appealing to do anyway.
Like I said before, though, my friend's store is really its own beast, and he has no experience in small or low volume stores. If your store is immaculate and there really is nothing to do, enjoy being paid to do very little to be in a certain location walking around.
