I'd love to know more about what you mean. The Impressionists were much later than the Classical period in music; usually it's defined as beginning around the 1860s in visual art. It's important to note that the two composers most commonly labeled "Impressionist," Debussy and Ravel, both hated the term, with Debussy stating

I tried to make ‘something else’ of them and to create—in some manner—realities—what imbeciles call ‘impressionism,’ a term as poorly used as possible, especially by art critics...

Debussy in particular was inspired not by the paintings of Impressionism but by the Symbolist poets, and one of his most famous works, Prelude to the Afternoon of a Faun, is based on a Mallarmé poem.

I think what you might be getting at, though, is actually the "Romantic" period, generally used to describe music from 1820 through the start of the 20th century. It's true that art song flourished in that period, with Schubert (more of a transistion figure), Schumann, Brahms, Berlioz, and more contributing significantly. But there's plenty of it before that, too, with Haydn and Mozart being two leading examples of classical composers who wrote solo vocal music based on poetry.

"Lyrical" also usually means something different in the context of classical music than how I think you're meaning it here. Generally, "lyrical" describes music that conveys a strong sense of emotion, especially in a personal way. This is certainly true of many Romantic composers who composed based on poetry, but it by no means confined to them.

So, in any case, I'm not quite sure how to answer your question without some clarification as to specific composers, time periods, pieces, etc.