I can't find any thing in Letters or HoMe about Pippin dying at that time. As best I can tell, Tolkien may have very briefly considered killing one Hobbit and then quickly dismissed the idea.
I did, however, find this in Letters:
[Of C. S. Lewis's comments on The Lord of the Rings:] ‘When he would say, “You can do better than that. Better, Tolkien, please!” I would try. I'd sit down and write the section over and over. That happened with the scene I think is the best in the book, the confrontation between Gandalf and his rival wizard, Saruman, in the ravaged city of Isengard. ’
I do not think the Saruman passage ‘the best in the book’. It is much better than the first draft, that is all. I mentioned the passage because it is in fact one of the very few places where in the event I found L's detailed criticisms useful and just. I cut out some passages of light-hearted hobbit conversation which he found tiresome, thinking that if he did most other readers (if any) would feel the same. I do not think the event has proved him right. To tell the truth he never really liked hobbits very much, least of all Merry and Pippin. But a great number of readers do, and would like more than they have got. (If it is of interest, the passages that now move me most - written so long ago that I read them now as if they had been written by someone else - are the end of the chapter Lothlórien (I 365-7), and the horns of the Rohirrim at cockcrow.)
If Lewis did not much like Merry and Pippin, it is hard to imagine him strenuously objecting to Pippin's death, when he apparently regularly suggested that Pippin be cut out.
Various drafts and outlines from HoME don't seem to indicate Pippin was in any trouble. In some, Merry and Pippin are not even present.
The chief differences from the final story were the coming of the Ents (with Elves of Lórien) to the Morannon (with an express declaration by the ambassador of Sauron that the Ents shall help to rebuild Isengard), uncertainty whether Merry and Pippin were present, and the person of the ambassador: doubtfully identified as the Wizard King (implying a different view of the outcome of his encounter with Éowyn and Merry in the Battle of the Pelennor Fields), but certainly a Nazgûl (‘flinging off his garments he vanishes').
It is difficult to disprove something of this nature, but given its absence in Letters or any indication of such plans in HoME, and taking that together with Tolkien's style and themes, it seems awfully unlikely that was considered.
I have, however, found unsourced online references to the claim that Tolkien intended to kill at least one Hobbit, either Sam or Pippin, that date back to August 2003 - before the release of the movie - that also mention Lewis's intervention. So if it is untrue, it seems to be a fairly old rumor. That seems to derive from HoME VII, The Story Foreseen From Moria:
Sally from Minas Tirith. Gandalf drives Black Riders back and takes crossing of Anduin at Osgiliath. Horsemen ride behind him to Gorgoroth. Hear a great wind and see flames out of Fire Mountain.
Somehow or other Frodo and Sam must be found in Gorgoroth. Possibly by Merry and Pippin. (If any one of the hobbits is slain it must be the cowardly Pippin doing something brave. For instance—
But this seems to be a thought thrown away very early, since it did not rise to the level of a completed thought, nor does it appear in later outlines or drafts, and I cannot find any reference to Lewis.