The most common and most likely answer to this crossword clue is the 4 letter word SILL
I've seen this crossword clue in The Daily Telegraph
S
I
L
L
Buddy explains!

The straight part
We know that "one lies horizontally" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one lies horizontally = sill.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 SILL mean?
SILL noun- (also window sill) A horizontal slat which forms the base of a window.
- A horizontal, structural member of a building near ground level on a foundation or pilings or lying on the ground in earth-fast construction and bearing the upright portion of a frame. Also called a ground plate, groundsill, sole, sole-plate, mudsill. An interrupted sill fits between posts instead of being below and supporting the posts in timber framing.
- A horizontal layer of igneous rock between older rock beds.
- A piece of timber across the bottom of a canal lock for the gates to shut against.
- A raised area at the base of the nasal aperture in the skull.
- The inner edge of the bottom of an embrasure.
- A young herring.
- The shaft or thill of a carriage.