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Sorry not to have responded sooner! There are a number of books that deal with Bishop William Lamberton of St. Andrews. Among these is Ronald McNair Scott's "Robert the Bruce - King of Scots" 1989. Another is Evan MacLeod Barrons' "The Scottish War of Independence" 1914, which until recently, was the latest definitive work on the subject. Peter Traquair has just come out with a fabulous new study of the Scottish war of independence: "Freedom's Sword". All of these books are readily available, and contain varying amounts of information on Bishop Lamberton. Some sources, including the landmark reference work "The Scottish Nation" by Anderson, claim that it was Bishop Lamberton who actually crowned Robert the Bruce. Given that these two men were very close, and had the year before, entered into a personal pact of mutual support, it is highly likely that Lamberton, as the Primate of Scotland, would have crowned Bruce.