Changing train stations in Paris

I prefer the train because traffic in central Paris can be very slow. We once had a horrendous midday trip from St. Lazare to Bastille by cab where we got bogged down in traffic continuously. The train is fast and doesn't get caught in traffic. Three tickets would cost 1.80 each; use coins in machines at the station. Hang onto the ticket till you leave the station at Gare du Lyon as you may be asked to show your validated ticket at any time and fines are stiff if you don't have one. The ticket is validated when you put it in the stile to enter the system.

The metro takes about 22 minutes or so once you find it and get going. You would take the 4 to Chatelet and switch to the 14 which is just a stop or so from Gare du Lyon. While Chatelet is not the most lovely stop to transfer, the stations are very well signed you just follow the signs for 14 which are in little purple circles. The final corridor to a platform always lists the stops so you can double check that you are heading in the right direction. You have to be able to carry luggage up and down stairs in the stations and you have to be pickpocket proof i.e. no wallets in pockets and paying attention to purses and small bags.

Janet's right . . the Gare de Lyon is the very next stop on the 14 after Chatelet. (I went home that way last night! That thing whizzes across the city.)

Ratp gives many options including the previous one.
Another Metro route would be to take the No 6 line to Bercy then the No 14 line to Gare de Lyon, again one stop away. This route has advantages, first being that the No 6 Metro entrance is closer to where you get off the train at Gare Montparnasse. The No 4 line entrance is a long way away, although there is a moving sidewalk part of the way. The No 6 line is also partly above ground going to Bercy, so you'll get a glimpse of Paris. The No 14 line is the newest Metro line, so they built escalator and/or elevator access to the platforms, which is nice when toting luggage. This way avoids the zoo at Chatelet.
Also there is the 91 bus that runs between the stations. Pick it up just outside Gare Montparnasse and it drops you across the street from Gare de Lyon. No toting luggage up and down stairs in the Metro, but you do have to get the luggage on the bus and where to keep it is an issue unless you are traveling very light.
All of these routes take 30 minutes or less including walking time.
And a taxi is always a valid option.

You can look at ratp.fr/en for suggested routes. I prefer taking Metro Line 13 to (direction Asnieres-Gennevilliers Les Courtilles) to Champs-Elysées-Clémenceau and changing there for Line 1 (direction Vincennes) to Gare de Lyon. It's not as direct a routing as the Line 4 to Line 14 connection but there is less walking. You could also take Line 6 (direction Nation) to Bercy and walk about 15 minutes to Gare de Lyon or change for Line 14 there. There are lots of mass transit options for this trip and I think that all will get you there in less than 30 minutes under normal conditions.

oooh now that's an interesting option, JHK! I wouldn't have thought of that, but you're right it's a pretty darned good option.

Allyson, you can see that people have provided you lots of different options, all within the metro system (and generally, as Janet pointed out, usually better than possibly getting stuck in surface traffic).

When is your visit?

Thanks to all - great info and certainly seems like the Metro is a do-able option. We are traveling the last week of August, probably mid-day. Thanks again.

It should be fine then. French people like to go on vacation in August rather than sticking around to strike. And the EuroCup will be over in mid-July.