Scratching head in fire in lift (5)
I believe the answer is:
boost
'lift' is the definition.
(I know that boost is a more specific form of the action lift)
'scratching head in fire' is the wordplay.
'head' indicates taking the first letters.
'in' indicates putting letters inside.
'fire' becomes 'boot' (I've seen this in another clue).
The initial letter of 'scratching' is 's'.
's' put into 'boot' is 'BOOST'.
'in' is the link.
(Other definitions for boost that I've seen before include "Increase, amplify" , "Shot in the arm" , "Increase (strength or morale)" , "Increase or encourage(ment)" , "Encourage; push up" .)