The most common and most likely answer to this crossword clue is the 10 plus 5 letter word HEARTBREAK HOTEL
I've seen this crossword clue in The Guardian
H
E
A
R
T
B
R
E
A
K
H
O
T
E
L
More clues leading to the result HEARTBREAK HOTEL
Buddy explains!
The straight part
We know that "King’s noted lodging" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case king’s noted lodging = heartbreak hotel.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.