BS 5839-1:2002, 22.2,c) '' Other than in category L4,L5 and P2 systems, if any flue-like structure, open stairway, shaft for a lift, escalator or hoist or any enclosed chute, penetrates one or more ceilings, a fire detector should be sited at the top of the shaft or enclosure and, on each level in the accommodation area within approximately 1.5 M of the penetration. There is a further note inviting consideration for cat L5&P2 system design.
Therefore the answer to your question is: perhaps. Consider the above rule on how the shaft is constructed through the building. Think about the shaft of a scenic lift ( like in the Scofield centre in Leeds ) where you may not need one. Consider the catagory of system design and you have your answer.
Regards
Dave