Wikipedia suggests May 1970 as the closure date of the main line platforms (following closure of Milnthorpe, Tebay and Shap on 1/7/68). I'm afraid that my records are very thin after the mid-sixties.
Carnforth main line platforms closed at the end of the Winter 1969/70 timetable on 3rd May 1970.
The last train to stop for passengers on the Down platform was a returning class 40 hauled enthusiasts charter from Edinburgh on 9th May 1970.
There are some good photos showing both mainline platforms on Railscot. Just google Railscot photos of Carnforth.
The ones of 4468 taken from a road overbridge by David Spaven shows what we are talking of very well. I was standing on the north end of the Up platform on the same day.
The photo of two class 90s northbound on the china clay tanks taken 20-1-2016 is taken from what was the Up platform entrance. More platform was removed than I remembered.