The most common and most likely answer to this crossword clue is the 8 plus 5 letter word PLATFORM SOLES
I've seen this crossword clue in The Times
P
L
A
T
F
O
R
M
S
O
L
E
S
Buddy explains!
The straight part
We know that "that give one a lift" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that give one a lift = platform soles.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.