As long as a coin is listed on exchange and I am sure there would be a miner for it and about the profitability, it is just a fluctuating one like when I last checked price of litecoin in terms of BTC, it peaked up to 0.0011 BTC but right now trading around 0.0008 BTC. And in dollar values it is around 90 USD. So, miners will mine and hold some portions after covering their mandatory expenses to see some profits.

Litecoin is currently ranked 21 in coinmarketcap which means I guess it will survive for few more years and I remember somewhere I read like Elon type of whale may adapt litecoin and pump like he did the same with dogecoin. I agree with that because such whales need a coin to manipulate and profit and they will not mind it is doge or lite.