The Potters have maintained their Premier League status since they were promoted in 2008.
Lambert, who has signed a deal until the summer of 2020, replaces Mark Hughes, after the Potters suffered a humiliating third-round FA Cup exit at the hands of League Two side, Coventry.
It is going to be even more hard to stave off relegation for Stoke with lots of the teams above them managing to scrape wins.
Stoke, of course, are without a permanent manager before the Man United game.
THIS game takes place on Monday, January 15. The onus is now on Eddie Niedzwiecki who has been in temporary charge since and he must find a way to rally his troops ahead of a daunting trip to Old Trafford.
The last time Stoke won at Old Trafford was 1976 and it might be a long old wait yet if Lambert is unable to turn things around.
In between the two first-half goals, Stoke had some moments of hope with injury-plagued Stephen Ireland, starting a league game for the first time in 996 days, coming close twice in quick succession, placing shots wide from no more than 15 yards.
Stoke City's Erik Pieters (thigh) and Bruno Martins Indi (groin) are back in training, though caretaker assistant first-team coach Kevin Russell does not know if the defenders will be fit for Monday.
Eric Maxim Choupo-Moting, who scored twice against United earlier this season in a 2-2 draw, also saw a goalbound shot blocked by Phil Jones. United should make home advantage count against a struggling Stoke side still seeking a fresh direction after Hughes' dismissal.
United goalkeeper David De Gea was needed to pull off a couple of good saves from Xherdan Shaqiri and Mame Biram Diouf.
The form of Lingard, Martial have eased the burden on Lukaku in a way Ibrahimovic never got to experience last season, and their link-up in play in the final third will be crucial to breaking down the visitors on Monday night.