The Us have been on the lookout for a new boss after parting company with Geraint Williams last month following the club's disappointing start to life back in League One this season.
Lambert, 39, who has been out of management since leaving former club Wycombe Wanderers at the end of last season, was the outstanding candidate, according to chairman Robbie Cowling.
The former Scotland international midfielder walked away from the Chairboys after two years in the hot-seat following their defeat in last season's League Two play-offs.
"I think that we had a massively high calibre of candidates who applied and showed an interest," Cowling said.
"We narrowed those down and interviewed four candidates from there."