The most common and most likely answer to this crossword clue is the 9 letter word PIGGYBACK
I've seen this crossword clue in Financial Times
P
I
G
G
Y
B
A
C
K
Buddy explains!

The straight part
We know that "Lift" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lift = piggyback.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 PIGGYBACK mean?
PIGGYBACK noun- A ride on somebody's back or shoulders.
- An act or instance of piggybacking.
- To attach or append something to another (usually larger) object or event.
- To obtain a wireless internet connection by bringing one's own computer within the range of another's wireless connection without that subscriber's permission or knowledge.
- To utilize "last-mile" wiring rented from a larger owner ISP by a smaller ISP.
- To carry someone on the back or shoulders.
- To transport (a lorry/truck) on a flatbed railway waggon
- To enter a secured area at the same time along with someone having authorized access; to tailgate
- On somebody's back or shoulders.
- Pertaining to transportation of goods where one transportation unit is carried on the back of something else. For example, a truck on a train.
- On somebody's back or shoulders.