Historically speaking, Litecoin has tended to follow Bitcoin's price trajectory but in a much more exaggerated manner (actually this is true for most altcoins). When Bitcoin went from $13 to $1,200 in 2013 (i.e. a 100x difference), Litecoin went from $0.07 to $48 in the same period (i.e. a 700x difference). When Bitcoin went from $900 to $300 in 2014 (i.e. a 66% drop in value), Litecoin went from $20 to $2 (i.e. a 90% drop in value).

Of course, there is no guarantee that history will repeat itself, and it's possible that LTC prices will continue to fall despite a rising BTC price (certainly the altcoin market is a lot more competitive now compared with 2011-2013 and the development of scrypt ASICs has also eliminated one of Litecoin's main benefits over Bitcoin).