Various newspapers covering frozen water on lake is invaluable (9)
I believe the answer is:
priceless
'is invaluable' is the definition.
(synonyms)
'various newspapers covering frozen water on' is the wordplay.
'various' becomes 'l' (I am not sure about this - if you are sure you should believe this answer much more).
'newspapers' becomes 'press' (the press is the newspaper industry).
'covering' indicates putting letters inside.
'frozen water' becomes 'ice' (I've seen this in another clue).
'on' is an insertion indicator (as in clothing 'on' a person).
'press' enclosing 'ice' is 'priceess'.
'l' put inside 'priceess' is 'PRICELESS'.
'lake' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for priceless that I've seen before include "Very precious; highly amusing" , "Very precious; absurd" , "Totally absurd" , "Wonderful" , "of inestimable worth" .)