I think LTC will grow up because people love to mine. Even people who just bought ASIC will keep their GPU to mine whatever they could. And LTC is the perfect way to do that. I'm talking about people with small rigs, who mines for fun (and for money too ), but more for fun.

Litecoin first will be a way to obtain Bitcoins with GPU mining in ASIC era, but due to that use will grow up to become the first altcoin and coexist with BTC.