The most common and most likely answer to this crossword clue is the 4 letter word TILT
I've seen this crossword clue in Financial Times
T
I
L
T
Buddy explains!

The straight part
We know that "lean over" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lean over = tilt.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 TILT mean?
TILT noun- A slope or inclination.
- The inclination of part of the body, such as backbone, pelvis, head, etc.
- The controlled vertical movement of a camera, or a device to achieve this.
- A jousting contest.
- An attempt at something, such as a tilt at public office.
- A thrust, as with a lance.
- A tilt hammer.
- To slope or incline (something); to slant.
- (jousting) To charge (at someone) with a lance.
- To be at an angle.
- To point or thrust a weapon at.
- To point or thrust (a weapon).
- To forge (something) with a tilt hammer.
- To play worse than usual (often as a result of previous bad luck or losses).
- (of a machine) To intentionally let the ball fall down to the drain by disabling flippers and most targets, done as a punishment to the player when the machine is nudged too violently or frequently.
- A canvas covering for carts, boats, etc.
- Any covering overhead; especially, a tent.
- To cover with a tilt, or awning.