The poem consists of lines that were jotted down by Coleridge when he was sitting in a garden, so it has kind of a spontaneous feel. The Romantics and Coleridge especially were the kind of writers who scribbled works of genius down in the nineteenth-century British equivalent of coffee breaks (tea breaks?). This poem was originally included in a letter, so it was not meant as a something to be published widely.
"This Lime-Tree Bower My Prison" consists of three stanzas of uneven length written in blank verse. An invention of the English Renaissance, blank verse has been used famously in Shakespeare's plays and in Milton's Paradise Lost. It has a regular meter, iambic pentameter, but no rhyme scheme. Iambic pentameter is the most common meter in English-language poetry. Each line has five "units" of an unstressed syllable followed by a stressed one:
No plot so nar-row, be but na-ture there (line 62)
It is fitting that the iambic pentameter in this poem is not very regular – Coleridge was more interested in capturing the mood than in counting syllables – and many lines have 9 or 11 syllables. Coleridge's buddy William Wordsworth also wrote a mean blank verse in his long poem, The Prelude.
In the Renaissance, blank verse was used in plays and other dramatic poems because it allows for a conversational tone that doesn't feel all formal and "Look-At-Me-I'm Speaking-In-Poetry." Coleridge knows this, of course, and it's no coincidence that "This Lime-Tree Bower My Prison" is a "conversation poem," or a poem where the speaker is supposedly speaking with a specific person. That person is Coleridge's friend Charles Lamb. In order to give the sense (somewhat) of conversation, he uses lots of enjambment, where one line carries over into another without a pause, and you'll also notice that the stanzas seem to break-off in the middle of a line and then pick up the meter using indentation at the start of the next stanza. This, too, was common practice in Renaissance plays. Open up just about any Shakespeare play and you'll see what we mean.