Directions Gare du Lyon to CDG

I'd take a bus even though it's 18€, it's nonstop, you won't have to watch your bags, and the RER train goes through some sketchy areas.

https://www.lebusdirect.com/en/2018/05/14/visit-paris-line-4-bus-direct.html

Tickets on the RER cost 10.30€ each.

• From Gare de Lyon, take the first westbound RER A regardless of destination: Cergy, Poissy, or St Germain en Laye.
• At Châtelet les Halls, the first stop, disembark and walk across the quai for the RER B to Roissy/aéroport Charles de Gaulle. Do not board the train to Mirty Claye if you see one. The airport trains and the Mirty Claye trains both depart from the same platform. Next train destinations are clearly marked on the monitors, just be aware.
• Exit the first stop at CDG, the stop just after Parc des Expositions if not on the express. The first CDG stop, called Roissypôle is for Terminals 1 and 3. To exit the terminal, you will need your ticket so do not lose it.
• Follow the signs to the CDGVAL, a free rail shuttle which will take you to Terminal 1 from where United departs.
  

If you are traveling on a strike day, the information above about boarding the RER B will be incorrect. If traveling on a strike day, either take a taxi at 50€ fixed fare or take le Bus Direct to terminal 1 at 18€ each. Le Bus Direct leaves from the street directly in front of Gare de Lyon.

I always take the RER. I've never worried about the area it goes through. Yes, people get on and off on their way to their jobs. There may be some thieves in the mix, they are there for tourists, always wise to keep track of your things. That's true of crowded metros anywhere in Paris, but especially those close to tourist frequented areas.

If the difference in price is not a deterrent for you, I'd say take Le Bus Direct. It's comfortable, no worries about luggage or thieves, no changes, no strike days. You get on right at Gare du Lyon and it takes you right to CDG.
Le Bus Direct = 18 €
RER = 10.30 €