Lamba also added 59 runs with Sourabh Chouhan (35) for the second wicket before joining hands with Ashok Menaria (42) to put on 87 for the third wicket.
Put in to bat, Odisha were restricted to 162 for seven in their allotted 20 overs with Chandrapal Singh (2/12) and Manjeet Singh (2/36) taking two wickets each.
Odisha lost openers -- Anurag Sarangi (21) and Roshan Kumar Rao (10) -- and Biplab Samantray (4) to be struggling at 49 for three before Govinda Podder (61) and Shesdeep Patra (13) steadied the boat for a brief period.
Podder, whose innings came off just 44 balls studded with seven fours and a six, fought single-handedly even as wickets kept falling at the other end.
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With Odisha reeling at 120 for seven, Podder found an able partner in Suryakant Pradhan, whose eight-ball 28 enabled Odisha cross 150-run mark.
Pradhan then hit back to trouble Rajasthan with the ball, seeing off Suryaprakash Suwalka in the second over of the chase before Lamba along with Chouhan and Menaria guided the team home with two balls to spare.