Litecoin is a promising coin, but its technology is outdated. Over the years, Litecoin will definitely grow, but I'm not sure it will cost $1000.
I don't know what you mean by "technology is outdated" .. For users, the most important is transaction speed and fee. At the moment, Litecoin is much more useful for ordinary users than Bitcoin or Ethereum.
I believe that Litecoin will never take the Bitcoin position, but if Bitcoin someday reaches a price of $100k, the price of $1000 for 1 LTC is very possible.