Attaching a cropped pic of the flower, if that would help.
Could be N. lanceolata,
I could not find this species in efi? Does it have any synonym?
Looks different from Nesaea lanceolata (Heyne ex Cl.) Koehne syn. of Ammannia lanceolata B. Heyne ex Wall. as per Catalogue of Life and Flora of Karnataka
May I request you to pl. post high resolution images to see the details.
Attaching one more image