Best Type of Transportation from Paris CDG to Gare de Lyon?

Trains all the way.

There are a number of direct TGV trains to Aix from CDG so it is not necessary to go from the airport to Gare de Lyon if one is convenient.

Agreed that you should look into trains from the airport. However, to answer the question in your title:

The easiest way, or the best way with a lot of luggage, is to just take a taxi from CDG airport. Gare de Lyon is on the right bank of Paris so the flat fare will be €50. No extra charges for the second person or for your luggage.

The cheapest way, which is what I would do if I were traveling solo and with just a carry-on, is to take the RER B from CDG airport station to Gare du Nord, then transfer to the RER D train to Gare de Lyon. This is a cross-platform transfer, i.e. you get off the RER B train and the RER D train (in the correct direction for this trip) is right across the platform on the other track. The cost per person is €10.30, or €20.60 for the two of you.

(You can also transfer at Châtelet Les Halles to an RER A train, and it is also a cross-platform transfer, so not a big difference either way.)

If you end up on the RER, remember that you need to keep your ticket all the way through the end of the trip (you will need it to exit the faregates, plus you can get fined by a ticket inspector if you are unable to produce the ticket.)

You can also transfer at Châtelet Les Halles to an RER A train, and it is also a cross-platform transfer

Through Friday the 30th, the RER A is closed between Vincennes and Auber. If you are traveling this month, transfer at Gare du Nord.

tnx to all who gave us info...tis much appreciated

My recollection of our visit to Paris 7 or 8 years ago is that we took the Air France Coach that goes from CDG to Gare de Lyon. We used the coach because the bus has an underfloor luggage compartment and we were carrying extra gear for a bike tour later is our trip. I didn't want to be pulling a gear bag and holding on to my wallet on the RER.

https://www.about-paris.com/air-france-coach-line-4-cdg-paris.htm

'Line 4' coach to Paris from CDG. Air France's Line 4 coach service
'Les Cars' from Charles de Gaulle airport gives you the option of
arriving at either Gare de Lyon and Gare Montparnasse railway stations
in Paris. Making it a good service if you need to continue your
travels by train.

Fares:Single: € 17 Return: € 29 Children (2-11): € 8.50 .No charge for
children under 2 Youth fare ( under 25 ) and for groups of 4
passengers or more € 14.50

https://www.lebusdirect.com/en/lines-and-schedules/cdg-airport-paris-gare-montparnasse-line.html

I just used the LeBus Direct in June to get from Gare de Lyon to CDG, so it is definitely a good option going the other way too. Easy to find, you can pay the diriver, and it was easier with luggage. It drops you off right in front of Gare de Lyon station.

Agree about LeBus direct. We just did it a few days ago and it was very convenient.

One more vote for LeBus Direct. Took it the other direction - from Gare du Lyon to the airport. Timely, good baggage storage and service and the tickets are good for 18 months or something on the route so you can take "the next bus" with the ticket you have without worrying about a specific schedule.

Information on-line: https://www.lebusdirect.com/en/lines-and-schedules/cdg-airport-paris-gare-montparnasse-line.html

Buy on-line and use whenever. You just need to know what terminal you're coming in from or leaving from but the price is the same.
Bus stop is directly in front of Gare de Lyon. The information page has detailed instructions on where the bus stops are at each terminal.

=Tod