Lomax was believed to be the leading female candidate for the role, after the vacancy was advertised in The Economist in recent weeks.
Speaking to BBC’s Radio 4, she said she will not be applying for the post, which she described as a “huge role”.
The economist served on the Monetary Policy Committee and was deputy governor from 2003 until 2008, leaving just before the Lehman Brothers collapse.
“We knew that something bad was happening, but we really didn’t know, and couldn’t really imagine how bad it was going to be. I mean, I left the bank just before Lehmans collapsed and it’s got a lot more interesting since I left.”
Earlier this month, another front runner Jim O’Neill, chairman of GSAM, ruled himself out of applying for the governor’s job.
King will step down in June 2013.