The most common and most likely answer to this crossword clue is the 3 plus 7 plus 8 letter word OLD ENGLISH SHEEPDOG
I've seen this crossword clue in Financial Times
O
L
D
E
N
G
L
I
S
H
S
H
E
E
P
D
O
G
More clues leading to the result OLD ENGLISH SHEEPDOG
Buddy explains!
The straight part
We know that "we should let him lie" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case we should let him lie = old english sheepdog.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.