Apparently, Astarte/Athtart/Ashtart the Phoenician/Carthaginian goddess was a variation of (or that she simply derived from the same religious figure) the Babylonian Ishtar (who was herself a fusion of Inanna and some Akkadian goddess named Ištar), but what of Anat(h)?
As it was shown in the texts regarding Baal, another Phoenician deity sometimes depicted as Astarte's consort, Anat and Ishtar share various similarities as both were worshipped as war deities and the former, though not as explicitly as the latter, seemed to have some attributes that were considered sexual (it was described that she and Baal grabbed each others' genitals, similar to the erotic description in Inanna and Dumuzid's courtship).
Another similarity was when Anat complained to El, which was itself similar to Inanna's threat to Anu...and last was her descent to the underworld, though she wasn't trapped there as Inanna/Ishtar was in Sumerian myths, her goal was the same: to find her consort, and that, was almost identical to the earlier myths of Inanna when she sought not to take her sister's throne but to resurrect her lover Dumuzid.
Besides all that, I read the article here which claimed Astarte and Anant may originally be a same deity, but ultimately split into two.
Their similarities seem to be the aspects of fertility, war, lions, and crescent. To ask the question more precisely, could Al-Lat, Anat/Anath, Ishtar/Astarte be seen as the "descendants" of an early Semitic goddess associated with love, war, and sexuality?