Well, if you look at the frontispiece to any edition of this collection of poetry by William Wordsworth and Samuel Taylor Coleridge, you will find a significant part of the answer! The collection is not actually called Lyrical Ballads. Its full title is actually Lyrical Ballads, with a Few Other Poems. This is a loose title which allows the authors of the collection a considerable amount of leeway, as essentially anything can fall under the designation of being an "other poem."
However, it's important to consider that "Tintern Abbey" is often considered a lyric. The lyric poem, though it has roots in a highly metrical and musical form in ancient Greece, has become defined in modern terms by its attention to the interior emotions and memories of a speaker using the first-person point of view. It might help to think of it in opposition to narrative or epic poetry, which tells a specific story; the lyric poem, in contrast, goes inward, examining the effects of a speaker's environment and surroundings on their emotional state. The Romantic period, of which Wordsworth was part, was instrumental in forming our current definition of the lyric poem.
Regardless of whether you consider the poem a lyric, though, we might ask how it fits thematically within the larger collection of Lyrical Ballads. A perusal of Wordsworth's preface gives some indication on this front. The preface to the collection identifies the key themes which unite the poems in the collection, beyond the mere fact of their form and type. The collection focuses on nature, the sublime, and the connection between the two—how the sublime can be found in nature "recollected in tranquillity." This is a major focus of "Tintern Abbey," which is about how the sights in the area of Tintern Abbey serve as a means of spiritual sustenance for the speaker—both in the past, when he was in London and away from the wonders of nature, and in the future, when he returns to the city with a new collection of memories.
Ultimately, this poem wins its place in the collection because it belongs there in terms of its content, concerns, and message.