Expose falsehood with this or let deceit run free
I believe the answer is:
'expose falsehood with this' is the definition.
The definition suggests a singular noun which matches the answer.
'let deceit run free' is the wordplay.
'run' indicates an anagram.
'free' becomes 'or' (I can't justify this - if you can you should give a lot more credence to this answer).
'letdeceit' with letters rearranged gives 'liedetect'.
'or' acts as a link.
Can you help me to learn more?
(Other definitions for lie detector that I've seen before include "Forensic equipment" , "Editor elect (anag.)" , "this could indicate a crime" , "way to discover fiction" , "Police polygraph" .)