Getting from Gare de Lyon to our apartment?

I say bite the bullet and take a taxi - not based on where you are staying, but based on my own experience of being jet lagged , tired and confused. Always feel it is money well spent to just get there and then take your time getting oriented.
Have fun

Thanks Diane. We won't be jet lagged as we'll already have been in Italy and Switzerland for two weeks before ending our trip in Paris. Do you still advise a taxi though?

Day train from Switzerland jet lag will not be a problem.

Yes your route is good.

Another option would be to walk across Pont Charles DeGaulle to Gare de Austerlitz - take the RER C to the Champ du Mars - Tour Eiffel stop. After a long train ride the walk might be nice if the weather is nice.

Christi, that sounds interesting. How long a walk is it and how easy is it to get to the bridge from Gard de Lyon station?

Depending on the location of the apartment, it might be faster and easier to take the Metro from Gere de Lyon to Ecole Militaire. This route is from the RAPT website. If you have a smart phone, download their free app for routes through the City of Light.

Cindy - the bridge across the Seine is in right next to both stations - its about a 12 - 15 minute walk.

Check it out on google maps: If you try gm directions it will route you the long way but you can just walk straight away from the train station to the bridge. Exit the station - cross Rue de Bercy - to Rue Van Gogh and across bridge - lovely view of the river

https://goo.gl/maps/LPvn9Y33mV22

Thanks Christi, that does sound lovely if the weather is nice. I take it the bridge is easy to walk across with suitcases?

Philip, Ecole Militaire isn't that close to our apartment. The closest metro stop appears to be either Bir Hakeim or Dupleix.

Yes - there is a wide walkway across bridge - I will guess you will not be the only one crossing with luggage.

Perry, first suggestion as in take a Taxi .......or my idea of RER A and then Metro #6?

I've done the walk with a large roller board (larger than carry-on size) and a backpack and it ain't bad. Not raining though.

The nice things of TGV’s is that they have windows, so you can see how the weather is at the moment you arrive in Paris.........
I would take RER A and Line 6 too as RER has lesser stops and so is in general better for the longer distances.

I would take the Line 14 one stop in the direction of Olympiades to Bercy.

Transfer to the Line 6 in direction of Charles de Gaulle/Etoile several stops to your stop Bir Hakeim.

That's a lotta stops on the line 6, but at least you get on it and settle in for the duration!

Or, you could make things even more simple and take the 87 bus from Gare de Lyon to Champ de Mars and walk about 10 minutes to Bir-Hakeim. There's usually enough room to stand with your luggage in the area designated for wheelchairs and strollers. If you need tickets, they cost 2 EU each when bought from the driver. The bus ride will take about 45 mins, and you'll walk about 10 minutes.
Here's how to do it:
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Thanks. I thought about the #87 bus, but I'm pretty sure we'll not want to stand for 45 minutes.

What's wrong with getting on line 6 at Bercy towards Dupleix? It's one stop or so on the 14 outbound, and the 6 is a lower stress line anyway than going inbound. I'm saying take line 6 clockwise rather than counterclockwise.

Once you're settled in, you will love strolling the 15th! Remember to go in the direction away from the Champ du Mars when you exit the metro stations and you will quickly find the shops and cafes that aren't depending on one-visit tourists.

There's an Alsatian boulangerie that will serve as a tasty transition from Swiss to Parisian pastry called Benoit/Maeder:
http://www.maison-alsace.com/bonnes-adresses/boulangerie-benoit-maeder

RATP shows it as a 13 minute walk to Bercy Metro, about the same as walking to Gare d'Austerlitz. Bir- Hakeim is an elevated station, so you walk down stairs to get to the street rather than humping the bags up the stairs at Champ de Mars.

If you board at Gare de Lyon, there might be plenty of seats for quite awhile. You park your luggage and sit nearby - or, if your luggage isn't too large, you can sit and keep it near you in the aisle. Since it's a long ride, you should head to the rear of the bus where you'll have enough room for yourselves and your luggage - and you'll get to see a lot of scenery, as well.

There's absolutely no guarantee that you'll be able to get a seat on the RER or Metro - depends on the crowds.

We (early 70s) returned yesterday and used taxis selectively: from/to CDG (fixed rate at E55), and occasionally when we were too beat at day's end to use Metro and walk the 6-8 blocks to our Latin Qtr apartment. Easy to hail, clean and comfortable, and drivers always courteous and patient with our fractured French. (A piece of paper with address clearly written was helpful one time when the driver admitted it was his first week driving in Paris.) The fares in Paris from tourist areas/sites never exceeded E10 - E15 with tip.) With baggage and, perhaps, some travel fatigue, I'd certainly consider a taxi on arrival in Paris.