The client calculates the priority of the transaction, which is defined as coin days destroyed (i.e. number of coins times coin age) divided by transaction size. If it is above a certain level, the transaction may be sent for free. Otherwise, a 0.001 LTC per KB fee is enforced by the client. In general, this also happens to be the minimum recommended fee per KB.
Some miners choose to enforce these fees and won't include a transaction in a block they mine if it does not have enough fees. Other miners don't care and include any transaction in their block.
As you can see in an example block, most transactions of any decent size don't require a fee. Generally, if you send 1 LTC which you did not receive very recently and is not composed of a lot of small input transactions, you do not need to pay a fee. If you try to send a transaction with zero fee when it needs one, miners might skip over your transaction, and you'll need to wait until some miner is willing to include it in their block. If you grow tired of waiting, you can broadcast another transaction using the same coins (but this time with a fee). It will be included in a block, and the previous transaction will be regarded as a double spend and thus be rejected and disappear from the network.