The most common and most likely answer to this crossword clue is the 9 letter word VESTIBULE
I've seen this crossword clue in The Daily Telegraph
V
E
S
T
I
B
U
L
E
Buddy explains!

The straight part
We know that "Lobby" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lobby = vestibule.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 VESTIBULE mean?
VESTIBULE noun- A passage, hall or room, such as a lobby, between the outer door and the interior of a building.
- An enclosed entrance at the end of a railway passenger car.
- (by extension) Any of a number of body cavities, serving as or resembling an entrance to another bodily space.
- To furnish with a vestibule or vestibules.