Despite a long history of short-term job exchanges between staff in agencies and client companies, this kind of deal has never before extended to such senior executives.
Lace insisted this week that the job swap would have real authority.
"We've made no firm arrangements yet, but it is definitely something we are working towards," Lace said. "My only worry is Drew will make a better job of running my business than I will of his."
The plan is for the pair to switch places toward the end of this year.
It follows job swaps between managers when Lace ran the Air Miles account at TBWA\London.
Air Miles moved to Grey last month as part of plans to evolve into a more broad-based travel service.
"A large part of that will be the communication strategy," Lace said. "Also, agencies talk a lot about understanding clients' business but to do that properly, you have to live it."
Leaders representing agencies and advertisers have been advocating a return to regular job swapping, which was once commonplace but is now rare.
Stephen Woodford, the IPA president, praised Lace and Thomson's initiative.
"Hats off to them. It's a very brave thing to do," he said.
Financial pressures leading to fewer people in agencies and client marketing departments, the polarisation of the ad industry between creative and media shops, and the risks involved have made exchanges almost non-existent.
- Perspective, p2.