"lead the project" is correct and can be used in written English.
It can be used in a sentence such as, "John was chosen to lead the project, which entailed a great deal of responsibility."
The Quakers asked Boehm to lead the project.
He refused but was eventually persuaded to lead the project.
The ODI and the Open University will lead the project with seven other organisations across Europe.
Frozen's joint directors Jennifer Lee and Chris Buck are on board to lead the project.
He asked Ali Hassan al-Majid, a general and a first cousin, to lead the project.
EDF will lead the project and obtain the initial upfront financing from banks and other investors.
They consulted with an architect, but soon Ms. Marxuach decided to lead the project herself.
Ofwat said Bazalgette Tunnel Ltd, a company formed to lead the project, would build the Thames tideway tunnel.
Most telling perhaps, though, is Bob Belleville, who was seduced by Jobs to lead the project team on the first Macintosh and who was subsequently ostracised.
