Ask Mr Google for the "definition of a lyrical book" and you will not get a definitive answer. The top results on my search turned up phrases like:
song-like, poetic, deeply evocative
beautifully full of emotion
effective use of poetic techniques
To the above, I say YES,YES, and YES! A well-written lyrical book contains all of these.
Two of my favorite lyrical books were written by Julie Fogliano. She is a former kindergarten teacher and an award-winning, New York Times best-selling author. Her picture books include a poetry collection and picture books that are rhyming and lyrical.
For me, two of her lyrical picture books stand out as stellar examples of how to incorporate the musicality of meter with occasions of rhyme and clever use of poetic devices. This combination results in these two books that emotionally connect with the reader and are so very satisfying to read.
The repetition is a poetic device called anaphora. In this case it emphasizes the child's barely-containable excitement. The last line here stops the reader one beat short of the established rhythm, which allows for a pause and breath before launching into the next burst of comments from the birthday child.
(Notice also the assonance of the vowels in "wishes" and "kisses", as well as the alliteration of B in berries/birthday and S in sandwiches and soup. More poetic devices!)
Altering line length
The last lines in the book are shorter than the preceding ones, which quickens the pace - the final push before the satisfying ending. They are infused with giddiness:
Can you feel the meter? The first word is a stressed syllable that is followed by two unstressed syllables. This pattern generally continues through the book.
Julie Fogliano uses more rhyme in this book than the birthday book. When the children in the book are finished with their imagining, they depart:
So back through the window
we climb as we wonder.
Back down the path that is tangled with thorns.
Back to the house where our dinner is waiting.
Back to the home that is cozy and warm.
(The rhyme here is a near rhyme ("thorns/warm"). An occasional use of near rhyme can work when it follows many pages of exact rhyme.)
The book ends by circling back to the original opening, contrasting the coziness of the children's home with the abandoned one they had found. This contrast stirs up emotions of both comfort and loss or sadness.
If you are interested in writing lyrical picture books, study books by authors like Julie Fogliano to see how they use meter, rhyme, and poetic devices. Rhyme Doctor Eileen Meyer has also been explaining poetic devices in a series of Poetry Prescription posts here on the HOUSE CALLS blog. Click here to read the post about anaphora.