Decision by lot, following Acts 1:26, was a Moravian practice stemming, like 'opening the Bible' at random, from belief in divine providence. Both were adopted by John Wesley even before his encounter with the Moravians; e.g at Oxford, and later, when in spiritual distress or perplexity, as in Georgia over Sophie Hopkey. It was part of his reliance on sriptural guidance, based on the practice of the apostolic church in Acts 1:23-6, and was his way of resolving his dilemma over responding to Whitefield's appeal to him to join him in Bristol in March 1739. Whitefield more han once chided him for resorting to the practice.
The Conference of 1792, quoting Prov. 18:18, decided by lot that the Sacrament would not be administered in the ensuing year. But the usage gradually faded out and in 1804 was rejected as a method of settling a dispute. Many Methodists continued to look for guidance by opening the Bible at random or used 'promise boxes' (which are still being produced).
The leader of the Bible Christians, William O'Bryan, was given to taking decision by casting lots, though not above ignoring the result if it did not suit him. At the breakaway meeting in Liskeard in 1829, presided over by O'Bryan and attended by five of the preachers, the drawing of lots, rather than majority voting (which had no scriptural precedent), was approved.