What is a "Lifeline Extension Belt"?
I think what the placard actually says is.

Lifeline
Extension Belt

(ie, its 2 things, not one!)
An A320 equipment specification indicates the narrow OHB you reference as number 16. Which is titled &quot;Lifeline&quot;. This line is used to aid evacuation from the overwing exits and more details can be found in this answer
Extension belts are used for infants on their carers laps, an extra belt loops round the child and attaches to the carers lap belt.

(source: cabincrewsafety.com)