Yes, you can invest in litecoin. I believe that litecoin are one of stable coin. And the price will go to $1000 , but it take time. Currently litecoin price about $250, it just make 4x then will reach $1000. Ethereum touch $1000 take about 3 months, litecoin possible will touch $1000 in year 2018.
Please take notes, above only suggestion. Decision is on you, please do not put your whole fund invest into 1 coin.