This is of course no sound or definite truth, but to me, it seems like the exchange rate between Litecoin and Bitcoin is pretty consistent regardless of the exchange rate to the dollar. For example, the exchange rate on BTC-e during the Bitcoin crash the past few days hardly changed. It was around 0.02 BTC per LTC before, and it's around 0.02 after. What did change is the USD per LTC, which dropped from $4.60 or so before to the $1.90-ish yesterday and now $2.50ish today since Bitcoin's value is increasing again.

I actually traded about 0.5 BTC for LTC right before the crash, thinking it might be a good way to end up with more Bitcoins, but I think that was not a successful choice after all. At least those Litecoins they didn't really lose a lot of value (in terms of Bitcoins).

I know a couple months ago, a Litecoin was worth something like 0.002 Bitcoins instead of 0.02 like now, so obviously it varies. But, overall it seems like Litecoin tends to match Bitcoin rather than compete with it, in terms of value anyway.