The reason I knew this is that Bitcoin will go mainstream next year but its transactions are way too expensive and when volume picks up Bitcoin will not be able to handle the transactions size.
LTC and doge [together] solve the tx volume and high tx cost issues for Bitcoin.
I agree that if bitcoin gains more popularity, it'll likely pull the DOGE up. Simply, if someone put some effort to learn about bitcoin, than he/she is very likely to try the other cryptos as well, and DOGE is one of the most popular and easier to get.
Don't really see what's the strenght of LTC nowadays tho. Bitcoin is (was and will be) more popular as both, functional currency or investment. Dogecoin has low tx fees, creates more hype and reaches to a new people. Think LTC will be slowly losing its position.