Unproductive life's origin in lake under stone (7)

I believe the answer is:

sterile

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'unproductive' is the definition.
(thesaurus)

'life's origin in lake under stone' is the wordplay.
'life's origin' becomes 'l' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' is an insertion indicator.
'lake' becomes 'erie' (Lake Erie is one of the Canadian/US 'Great Lakes').
'under' says to put letters next to each other.
'stone' becomes 'st'.
'l' going into 'erie' is 'erile'.
'erile' put after 'st' is 'STERILE'.

Can you help me to learn more?

(Other definitions for sterile that I've seen before include "Uninspired" , "Bacteria-free" , "Lab so clean" , "Unable to have children" , "Unable to produce young" .)

I've seen this clue in The Telegraph.

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