Can you pay with Litecoin at any place that accepts Bitcoin? If no where can you spend Litecoins?
Merchants that only accept Bitcoin, will not accept Litecoin directly.
However you can pay any Bitcoin merchant with a 3rd party that automatically converts your Litecoin to Bitcoin. The most well known service of this type is shapeshift.io
Merchants can integrate their "shifty" button to make this easier for consumers to use, but the Shapeshift service is available for every consumer wishing to pay a Bitcoin merchant regardless of if they have integrating the Shapeshift API or not.
While the process of spending Litecoins is extremely similar to Bitcoins, it is an alternative currency without a community accepted fixed exchange to Bitcoin therefore the merchant has to accept the work of conversion.
To the best of my understanding, Bitpay, bitmit.net and the other major markets and payment portals do not accept Litecoin. I'll refer you to this discussion as it probably is more informed and active than anything you'll get in a stackexchange format https://bitcointalk.org/index.php?topic=139940.0