Who is the lead engineer at NASA?

Your question does not specify if you are asking who is the current lead engineer at NASA or who was the lead engineer at the time the story of Hidden Figures is set.
I should start off by saying that NASA does not have a position titled "lead engineer." Rather, individual projects have their own lead engineers. Adam Steltzner can probably be considered NASA's highest ranking and most well-known engineer. He is currently the chief engineer of the Mars 2020 project and a high ranking engineer at NASA's Jet Propulsion Laboratory.
As for the lead NASA engineer during the early 1960s when Hidden Figures is set, there were many engineers involved, but Robert C. Gilruth can probably be considered the lead engineer at the time. Gilruth is the primary inspiration for Kevin Costner's character of Al Harrison in the film. He headed up the Manned Spacecraft Center at NASA from its inception and directed the Mercury and Apollo projects. Of course, there were many other top engineers involved in these missions and Al Harrison also incorporates their stories as a composite character.
http://www.adamsteltzner.com/

https://www.nasa.gov/modernfigures/