Litecoin has been a nice alternative to Bitcoin in terms of speed, and inexpensive fees. With its implementation of SegWit before Bitcoin, it shows that LTC has better consensus over its network upgrades than the former. Even if Bitcoin implements Lightning Network, Litecoin will continue to become used in the future for extremely fast payments. Since it is silver to Bitcoin's gold, Litecoin will surely survive for many years to come.

As for Dogecoin, I have no idea why its price has increased exponentially over the market, since it has an inflated supply and it somewhat lacks active development. I know that DOGE has extremely cheap fees and it is ideal for micropayments but its current supply will greatly diminish its value over the course of time. Therefore, this price uptrend over Dogecoin may be temporary, but as long as it could provide usability among altcoins in existence, then it could survive for many years to come.

Another altcoin that might survive in the future would be NEM. Given that it is widely popular in Japan and has an outstanding development plan, (along with its features) it may remain in crypto land for the long-term. One of the greatest features that this altcoin has is its ultra low fees, along with speedy transactions, making it the ideal choice for mainstream payments without any congestion (unlike Bitcoin). But, it is only a matter of time before many of the altcoins would remain in existence with the support from their users. Just my thoughts