The most common and most likely answer to this crossword clue is the 2 plus 3 plus 2 plus 1 plus 4 letter word BY WAY OF A JOKE
I've seen this crossword clue in Financial Times
B
Y
W
A
Y
O
F
A
J
O
K
E
Buddy explains!
The straight part
We know that "lulz" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lulz = by way of a joke.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.