Chosen answer:It's possible that he wasn't experienced enough with it, or at least felt like he wasn't, to be of any use. Remember, in the first film, Luke's total experience in handling the lightsaber was only a few screen minutes before he, Han, Chewie and Obi-wan attempted the rescue. It's also quite probable that Obi-wan warned Luke NOT to carry the lightsaber during the rescue attempt; it was, after all, Anakin Skywalker's lightsaber. If Luke (Anakin's son) boarded the Deathstar armed with Anakin's lightsaber, that peculiar disturbance in the Force could potentially lead Darth Vader straight to Luke, rather than to Obi-wan.
Chosen answer: It's possible that he wasn't experienced enough with it, or at least felt like he wasn't, to be of any use. Remember, in the first film, Luke's total experience in handling the lightsaber was only a few screen minutes before he, Han, Chewie and Obi-wan attempted the rescue. It's also quite probable that Obi-wan warned Luke NOT to carry the lightsaber during the rescue attempt; it was, after all, Anakin Skywalker's lightsaber. If Luke (Anakin's son) boarded the Deathstar armed with Anakin's lightsaber, that peculiar disturbance in the Force could potentially lead Darth Vader straight to Luke, rather than to Obi-wan.