It seems to me that it's now inevitable (for better or for worse) that Dogecoin will become the bronze to Litecoin's silver, or in other words 3rd highest valued cryptocurrency.
Dogecoin has surpassed Litecoin's transaction volume in USD for the last two days. It's still finding its place in the world, and it's possible that place isn't 3rd.
I suspect Litecoin will fade into non-existence, with Peercoin (or some other somewhat novel approach to the problem) replacing it. LTC has nothing over Bitcoin...it's merely still mine-able on GPUs, which is good for miners that have GPU farms[1], but not all that useful for anybody else. Maybe it has value as an alternative blockchain to BTC, should something terrible happen to BTC, but many cryptocurrencies could provide that.
Doge is roughly identical to Litecoin, but more fun.
1-I have a modest GPU mining setup, and I mine LTC and Doge.