I cannot believe that a a small place like Catasfield had 3 or more LUCY Pipers, so you have some other problems.
The SFHG list of St Lawrence, Catsfield baptisms also show the baptisms of:
George Piper son of George (a labourer) & LUCY 2/5/1819 (info Henry John Park, the Crowhust Curate) and Elizabeth Ann Piper son of John (a laboureer) & LUCY 15/4/1821.
As these are seqential to the base born births you have to a Lucy Piper, are they all births to the same Lucy but with different partners?, (or was her husband Edward also known as George and John) or is it just some bad record keeping in the Catsfield registers?
Alternatively, could either of your two 1824 findings with less than 9 months between them, be baseborn births to another Lucy Piper who just happened to also be living in Catsfield?
Lastly, rather than a death, were there any male Pipers from the Catsfield area sent to Australia as transportees? (there was a Simon Piper in 1820, but I do not know where in Sussex he came from)
As I wrote, "You have some problems to sort?

"
Roy G