The most common and most likely answer to this crossword clue is the 9 letter word RHAPSODIC
I've seen this crossword clue in Financial Times
R
H
A
P
S
O
D
I
C
More clues leading to the result RHAPSODIC
- Romantic chap going out with Doris
- Like some music or, perhaps after initial cuts, like some poetry
- Carelessly I drop cash, being delirious
- Effusive, improvised C sharp setting for Groom’s Vow Rejected
- Lyrically romantic harp playing before disco dances
- Stealing hearts, music genre’s poetic and lyrical
- Card shop I went round for something lyrical or romantic
- Smash hit podcast on radio originally — completely timeless and joyful
- Excessively emotional chap Doris abandoned
Buddy explains!

The straight part
We know that "Lyrically romantic" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lyrically romantic = rhapsodic.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.