The appointment is not thought to affect the bank's relationship with RKCR/Y&R, the incumbent on the main £40 million advertising business.
WPP, the owner of RKCR/Y&R, is understood to be considering what, if any, action that it could take against the start-up on the grounds that the deal contravenes the agency's non-compete clause.
Both WPP and Adam & Eve refused to comment.
Lloyds TSB secured the first Tier One sponsorship, along with its sister brand Scottish Widows, in 2006.
The bank recently unveiled Jonathan Edwards, the triple-jump Olympic gold medallist, and Ade Adepitan, the Paralympic basketball player, as its official ambassadors for the Games.
Scottish Widows has already launched Olympic-themed TV ads, and is this year extending its above-the-line budget by 50 per cent in order to capitalise on its association with the 2012 Olympics.