The title of the poem comes from the second line comes from the second line of the 1834 revision of the poem, and the third line of the original version. The title has a catchy, arresting sound. Rather than saying, "This lime-tree bower is my prison" and making the metaphor super-obvious, Coleridge condenses the meaning so that you almost imagine a colon after "bower": "This lime-tree bower: my prison." If you automatically knew what lime trees were, as nineteenth-century British readers did, you would be drawn in by the implicit comparison between big, beautiful, leafy trees and prison walls. Updated into contemporary American-speak, the title might go, "These oak trees my Alcatraz."
Originally, the poem did not have a title. Coleridge sent it to his friend Robert Southey in a letter, as some "lines" that "pleased" him. It's like, "Hey, take a look at this. Neat, huh?" But then Southey published the poem in 1800 with the unnecessarily long title of "This Lime-Tree Bower My Prison, A Poem Addressed to Charles Lamb of the India House, London." Fortunately, the title of the poem was shortened when it was republished in 1834 as simply, "This Lime-Tree Bower My Prison."