It is not uncommon for the SNCF to offer connections between Parisian stations with a somewhat short time between two trains. For example, if you have less than 30 minutes to make the connection between Gare de Lyon and Gare de l'Est, this may not be enough in certain cases. Connecting between two Parisian stations can then become stressful, even more so when you come to Paris from time to time for professional reasons.    

We must not tempt the devil, especially as disruptions can occur on the metro or RER lines or heavy traffic can slow down bus traffic. Signaling breakdowns, passenger accidents, power outages are all reasons that can prevent metro lines from operating normally.   

It takes 20 minutes to go from Gare de Lyon to Gare de l'Est using lines 5 and 1 with a change at Bastille station. It is also possible to take bus line 65 for an approximate journey time of 30 minutes.   

By car, journey estimates remain approximate. They strongly depend on the traffic situation in the capital at the time you have your connection. In other words, the journey can last 15 minutes or 35 minutes, depending on the circumstances.