Lied when running out of capital (3,5)
I believe the answer is:
new delhi
'capital' is the definition.
(capital of India)
'lied when running' is the wordplay.
'running' is an anagram indicator (the letters run around to different places).
'lied'+'when'='liedwhen'
'liedwhen' with letters rearranged gives 'NEW DELHI'.
'out of' acts as a link.
(Other definitions for new delhi that I've seen before include "somewhere in Asia" , "It's novel in India" , "foreign city" , "Lutyens' design" , "Indian capital city" .)