Gare de Lyon Hotel

You're one metro stop away from the Bastille area, which will have more/better hotels than the immediate vicinity of Gare de Lyon. There are other/better areas of Paris to stay in, and you could take a cab if you don't want to try to take luggage on the metro/RER/bus.

Not too much luggage, I hope. There is a Mercure on the station, on the front right as you look at the station. Nothing great, but nothing particularly bad, OK brekkie, tiny tiny reception desk, a departure screen for the station in the stairwell near the brekkie room, you can't get directly into the concourse and go around the outside, scaffolding up when we stayed in May, probably down now; There is also a pretty good Holiday Inn just down the road 150 yards or so. I think they are called the Holiday Inn Bastile or some such. Old turn of the century building, several small elevators, pretty good brekkie, deals available sometimes, our room had a (very distant) view of the Eye-full Tower. There's also a Novotel on the station which we haven't yet given a try. Strange since we often pick Novotels. Haven't tried any of the Ibis locations nearby as we usually stay in an Ibis closer to the Eye-full Tower. Remember, when packing, less is more.

Thanks for the hotel info. Mercure was one of ones I'd considered. Do you think it is safer/more reliable to book the room thru a website like hotel.com, etc, than to book with hotel directly?

Nope, I always book through the Accor website or the Mercure website. Never failed me yet...

Where to make reservations: When booking thru a consolidator or other non-hotel site you might have a real bad time of it if anything goes wrong like overbooking, etc.
I check out all of the sites then go directly to the hotel web site to make my reservations as long as their price is in line with what I found on the other sites. This way, if anything does go wrong, I feel I have a much better chance of getting better service from the hotel to resolve the issue. We try to stay in B&Bs as much as possible so book them directly thru their own web site. Happy travels.