The most common and most likely answer to this crossword clue is the 7 letter word BASKING
I've seen this crossword clue in The Sunday Telegraph
B
A
S
K
I
N
G
More clues leading to the result BASKING
Buddy explains!

The straight part
We know that "Lying in sun" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lying in sun = basking.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 BASKING mean?
BASKING verb- To bathe in warmth; to be exposed to pleasant heat.
- To take great pleasure or satisfaction; to feel warmth or happiness. (This verb is usually followed by "in").
- The act of one who basks.