Courtesy Lahiri's well-made 108 off 212 balls and overnight centurion Arindam Das's 164 helped Bengal reached 431 in 166.2 overs.
For the Services, their off-spinner T Koteshwar Rao bowled a marathon spell grabbing four for 123 in 49 overs.
Left-arm spinner Rahul Kanojia bowled 39.2 overs and took two for 91.
At stumps, Services reached 39 for no loss in 11 overs with Pratik Desai batting on 24 and Anshul Gupta undefeated on 15. Services need another 393 runs in 180 overs (two days) to get three points from this match.
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The duo added 55 runs for the fourth wicket in the first hour as Arindam brought his third score of 150 plus in his 12-year career for Bengal.
The only rash shot that Arindam played during his 306 ball innings was an edge that flew over second slip for a boundary.
It was Rao who breached through Das's defence as he was bowled for 164. He faced 306 balls hitting 14 boundaries and a six. Lahiri however carried on confidently at the other end. He drove beautifully mainly through the cover region and also kept the scoreboard ticking with singles and doubles.
Playing his 100th Ranji Trophy match, skipper Shukla (28) looked confident from the start as he first hit an inside out cover drive off left-arm spinner Rahul Kanojia and the hoisted Rao for a six over long on. He added 55 runs with Lahiri for the sixth wicket.