To speculate on etymology a moment, perhaps this is a blend of the familiar pickle (English) and unfamiliar paco lilla (Indic), which I’d phrase more as “from paco lilla, influenced by English pickle”. Presumably of late 18th/early 19th century origin, given that attested from 1845, and we see paco lilla in 1805 Art of Cooking (which had appeared since 1747). Since the term also exist in the US for some similar, some different recipes, this suggest that various pickles were being made and named in US revolutionary times (dunno about extent of language interaction post-revolution) and later, and the term adhered to some of them.
Culinarily, the British (and some American) recipe feels pretty Indian, and turmeric is a pretty common Indian spice – compare aloo gobi, which is potatoes and cauliflower, which turmeric and others. There are obvious culinary words of Indic roots, such as mulligatawny (Tamil), also characterized by the yellow from turmeric, and this could well be one of them.
If anyone can add more details (esp. on Indic roots), that would be welcome, but I’ll keep my speculations to this talk page.