Lee, a 24-year-old homegrown player, was deputising for the injured Ben Foster, who is on loan from United, and produced a series of stunning saves to keep City at bay.
And it left City, who won so well at Aston Villa last week, still in search of back-to-back league victories for the first time in 14 months.
Despite picking up a valuable away point, Watford remain entrenched in the relegation places, but they will take heart following this battling display.
Unsurprisingly City fielded the same starting line-up which had registered their first away league victory of the season at Villa last week.
But it was all change for Watford following a miserable home defeat by Sheffield United. Aidy Boothroyd brought in 4 new players, though the absence of defender Chris Powell was enforced by suspension.
The fact the game remained goalless was mainly due to the brilliance of keepers Nicky Weaver and Lee, with each making two terrific saves in the opening quarter-of-an-hour.
Weaver made an acrobatic leap high to his left to claw out Damien Francis' looping header and then stretched out his left leg to divert Darius Henderson's effort to safety.
Lee, whose other main claim to fame has been an appearance on the television business reality show Dragon's Den, was not to be outdone as he excelled to keep out a low drive from Micah Richards and then a close-range header from Georgios Samaras.
Watford had a lucky escape early on when Francis was only booked for an elbow to the head of Joey Barton, when referee Mark Clattenburg could easily have produced a red card.
And Watford captain Gavin Mahon was lucky to go unpunished after leading with his elbow while also challenging Barton, who was pole-axed for a second time in the opening half-hour.
City's Bernardo Corradi was also fortunate to escape punishment after catching James Chambers with yet another flaying elbow.
After an eventful opening, the match quickly descended into a war of attrition with each side cancelling out the other.
But in first-half stoppage time Watford central defender Danny Shittu came within a whisker of giving the visitors the lead when he headed against the crossbar.
The second half lacked sparkle and for the opening 20 minutes both keepers were redundant. City boss Stuart Pearce then made a switch, taking off the ineffective Samaras for Ishmael Miller with Darius Vassell moving inside to partner Corradi up front.
When City finally conjured a decent opening they were again thwarted by the brilliance of Lee. The keeper flung himself low to his left to turn away a free-kick from Barton which curled around the defensive wall and then Lee did well to turn Corradi's follow-up round the post .
Late on, Lee made another stunning stop to deny Corradi, who also might have won a penalty when he went down in the box and TV replays showed DeMerit had tugged his shirt.