City's leading scorer Dean Windass had given the home side a deserved first-half lead but Carlisle replied early in the second half thanks to a horrible ricochet.
Kevin Gall had found himself in space on the edge of the box but his volley was going wide until it hit the unsuspecting Lumsdon leaving goalkeeper Donovan Ricketts stranded as it went past his out-stretched left hand.
The goal spurred on a Carlisle side that had done little in the first half to suggest that they could get back into the game.
Bradford had dominated the opening exchanges without creating too many chances and when the goal did come after 21 minutes it owed much to a terrible mix-up in the Carlisle defence.
David Raven and young goalkeeper Keiren Westwood - who had a two-game trial with Bradford at the beginning of Todd's tenure - got in each other's way on the edge of the box when there seemed little danger.
The ball then ran on to Bradford's talisman who struck a crisp volley into the roof of the unguarded net.
But Bradford could not capitalise on their advantage against a side yet to win on their travels this season and after they had pulled level it was the visitors who had the better chances.
Alan Rogers was forced to clear a Peter Murphy header off the line before the lively Karl Hawley fired a good chance into the side netting.
Both goalkeepers were forced to make smart stops in stoppage time as both teams hunted for the winner.