Why does ETH need its own litecoin? Litecoin can be ETH's litecoin.
Litecoin served a clear purpose -- it was the second digital currency that provided users an alternative to BTC. At this point, there are hundreds of alternatives and ETH users don't need another alternative to ETH, imo.
ETC will likely continue to exist as long as traders want to trade it but I don't think it serves a purprose for ETH the way LTC did for BTC.