Deny is the opposite of Believe. Believe is related to Religious. Religious is related to Parish. Parish is a type of State. 
Lie is related to Testimony. Testimony is related to Speech. Speech is related to Give. Give is related to Gesture. 
Deny <--Antonym--> Believe <--RelatedTo--> Religious <--RelatedTo--> Parish --IsA--> State 
Lie <--RelatedTo--> Testimony <--RelatedTo--> Speech <--RelatedTo--> Give <--RelatedTo--> Gesture 