The most common and most likely answer to this crossword clue is the 12 letter word MINNESINGERS
M
I
N
N
E
S
I
N
G
E
R
S
Buddy explains!
The straight part
We know that "they would wax lyrical" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they would wax lyrical = minnesingers.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.
What does MINNESINGERS mean?
MINNESINGERS noun- In 12th- to 14th-century Germany, a peripatetic musician, often performing songs of courtly love.