Lyons scored a 30th minute penalty for what was the only goal of a closely fought contest.
It was a disappointing result for a Harps side who up until last night, still held out hope of sneaking into the play-off positions at the top end of the division. However, with Galway winning on Friday night, they are now nine points off third spot.
Sean McCarron went closest to a Harps equaliser when he fired just wide close to the end. Rovers ended the game with ten men following the dismissal on the hour of defender, Conor Dunne, following a challenge on Keith Cowan.
After last night's game, Harps boss Ollie Horgan questioned his players' attitude and approach to this game, saying their performance was a wake-up call for everyone.