In her new role, she will continue to oversee Grey's new-business drive while taking over responsibility for its Diageo and Remington accounts.
News of her promotion coincides with an announcement that the agency has recaptured the Ben Sherman account, four years after the fashion brand parted company with Grey.
The re-appointment follows a period during which the agency presented strategic advice to Ben Sherman executives who want to shed the brand's associations with "yob" culture.
The company plans to spend between £4 million and £6 million on advertising to promote the brand in its key markets - the UK, the Americas and Australia.
Naked Ambition will handle media strategy.
Mendelsohn's elevation comes just over a year after joining Grey from Bartle Bogle Hegarty, where she had spent her entire career.
She is part of the senior management team led by Dave Alberts, Grey's chairman and executive creative director, who has been running the agency since Lace's exit in March.
"Dave and I have quite clear responsibilities," Mendelsohn said. "While he concentrates on our strategic vision, the job of driving and growing the business will be down to me."
Meanwhile, the agency has axed the jobs of six account managers. The redundancies follow the recent loss of the £55 million global account for the Pedigree Petfood dog food brands, which defected to TBWA\Worldwide earlier this year.