After earning a spot-kick, Lita then stalled his run up before watching goalkeeper Kieren Westwood deny him once and then twice, from the rebound, to leave Coventry in with a chance.
And when Marlon King, who spent time on loan at the Riverside in the club's relegation season, was presented with a penalty of his own 12 minutes from time, he converted showing Lita how it should be done.
It was a winner that leaves Middlesbrough still two points from the foot of the Championship by goal difference, while also leaving Tony Mowbray pondering how he can turn things around.
Lita's penalty was the key moment and provided Middlesbrough with the chance to make Coventry pay for their wastefulness in possession.
For all Jason Steele had to be alert to deny decent efforts on his goal, his solidity ensured there was a base for the Teesside outfit to grow at the opposite end.
Lita and Scott McDonald had already gone close with a couple of headers, but it was not until Julio Arca's clever chip towards the top corner was turned behind by Westwood that Middlesbrough had the confidence to press more.
But ultimately they also failed to make the most of the most perfect of chances just before the half hour mark. Lita was stupidly brought down in the area by defender Nathan Cameron as they chased Tony McMahon's long pass.
But Lita's ridiculous penalty, choosing to look at the referee during his run up, led to his poor spot-kick being saved by Westwood, who then somehow turned the striker's rebound effort up and on to the underside of the bar.
After the restart Marvin Emnes, starting his second match since returning from a loan at Swansea, became more effective. Two of his centres created chances for Arca and Lita, but neither made the most of the opportunities.
Middlesbrough, denied by Westwood again when Lita was faced with just the goalkeeper to beat after McMahon's pass, had the better of the second half. Coventry, though, occasionally had the attacks to sneak a win.
And win, once Emnes had volleyed against the bar, was exactly what they did when King slotted beyond Steele after Matthew Bates had brought down Gary McShefferey late on.
MIDDLESBROUGH (4-4-2): Steele; McMahon (Hoyte 78), Wheater, Bates, Bennett; Emnes, O'Neil, Bailey, Arca (Boyd 78); McDonald, Lita. Subs: Coyne (gk), Kink, Hines, Tavares.
COVENTRY CITY (4-4-2): Westwood; Keogh,McPake,Cameron; Wood, Gunnarsson (Eastwood 68), Doyle, Carsley, McShefferey (Clarke 83); Platt, King (Jutkiewicz 81). Subs: Ireland (gk), Bell, Cranie, Baker.