I came to know that there are two primary writing system lineages. Brahmic and Phonecian.
While I know that Indus script is not yet deciphered. I'm wondering if we at least know the lineage of Indus script?
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The answer seems to be no. Asko Parpola, in his chapter on the Indus script in Daniels and Bright's The World's Writing Systems (1996), says: "it has no obvious genetic affinity with any other known script... There is no connection whatsoever with the earliest scripts of historical South Asia, Brahmi and Kharoshthi, which were created on the basis of Semitic and Greek alphabets".
(Note that the last sentence implies that the "two primary lineages" you mention are really one lineage, though the question of the exact relationship between them, if any, is still debated.)