CDG to Paris, Gare de Lyon

A taxi would be 50€ fixed rate to Gare de Lyon from CDG.

But you can just take the "Bus Direct" which is a nice bus that will take you direct to Gare de Lyon (the bus' end point is Gare Montparnasse; gare de Lyon is the first stop).

A bit cheaper, and comfortable and safe and gets you where you need to go without changing.

Taxis waiting at the airport taxi stand cost a flat fee of 50 euros and don't require any reservation or meeting up with a specific person. The other alternative that I've chosen as a single traveler is the Le Bus Direct Line 4.

Passport control time could be brief or could take up to an hour if they don't have enough staff to match arrivals. If you have 2 hours to navigate the airport, 1 hour for the taxi ride, and 1 hour for surprises, then 4 hours is enough time to get to Gare de Lyon, assuming no significant flight delay. Most pre-purchased train tickets are no good if you miss the scheduled train.

I see that you had similar responses on this earlier version of your question.

We're in a similar situation (different train station) and have decided that a taxi is the best solution for us. It's a fixed rate and a defined pick-up location. (I'm not sure how that works with Uber at the airport). But the other posters are right, le Bus Direct is probably a better (and slightly cheaper ) alternative. They run pretty frequently, but you may have to wait at the airport, both for the bus to arrive and then for it to pick up at other airport stops.
You don't have lot of time to spare in your schedule. Assume an on-time arrival (nothing guaranteed there) and approximately 2 hours to clear customs, pick up luggage and get to the taxi stand. Then an hour to Gare de Lyon (could actually be a little less since by then rush hour would be over). That puts you at the station roughly an hour ahead of time. Getting out of the bus is not getting on the train, so allow some time to find your track, etc. (I'm assuming you are familiar with that station - if not, allow a little more time) and you should be okay IF all of the built-in time assumptions are accurate (plane arrival, airport navigation, traffic, and the unexpected).

If you assume an on-time arrival, I usually take about an hour from the time lands to when I've deplaned, gone through immigration, retrieved all my luggage (because I'm bringing stuff BACK when i go home to the States) and have walked out the front door of the terminal. It can take two hours, but that's really the exception. I don't think you have to assume it will take that long.

If you then figure half an hour to find the bus, wait for one, and get on it, and then an hour into town, you're perfectly fine for a noon train.

Of course you can never know for sure ahead of time if your flight is going to be on time!

I would suggest you take a taxi. You only have about 4 hours - not much leeway for things to go wrong.
You never know how long it is going to take to get through customs/immigration and for your luggage to come thru. For us, it was over 45 mins for the luggage.

Even though the bus is easy and goes directly to the train station, we waited over an hour for the bus to come. We were not in a rush but you might be tight for time if this happens to you.

Best to take a taxi.

I was just there - the Direct Bus is nice and costs $14-$17. RER (B) is 10 euros and goes to the Denfert Rochereau train/metro station. Note that RER is the regional train system (also used by locals) and can be very busy during peak times.
If you can take a taxi for $50 for 2 to Gare de Lyon - that would be a deal (no transfers or schlepping from one metro line to another).