It does have something to do with plumblines, and like a lot of expressions, it dates back to our naval past. When a sailing ship was sailing through narrow waters, a designated sailor would have the duty of casting a rope weighted with lead over the side. The rope was of a specific length, and the sailor could judge from his casts the depth of the water, and help the helmsman to avoid shallows or sandbanks which would run the ship aground. The job of 'swinging the lead' was one of the easiest tasks on board, especially as it could coincide with the rest of the crew having to constantly re-set sails, or even in some circumstances, row with oars which was back-breaking work. So, 'swinging the lead' became a favoured occupation of the more idle crew members, and the term has become synonymous with people who like to do as little as possible, while others are working harder.