I can see that I can buy litecoins from btc-e, but they charge a fee. My question is, how are they buying litecoins, i.e. I am assuming they are buying litecoins without paying a fee, and would like to know how to buy litecoins without paying a fee.
BTC-E does not BUY LTC.
They just have Buyers and Sellers.
When you buy 1 LTC you do not buy it from BTC-E but from Sellers which are on BTC-E (for example you (Bob) buy 1 LTC on BTC-E. BTC-E make you buy it from 2 sellers (Gerard and Bernard)).
BTC-E takes fees for the 'link' between you (buyer) and the sellers. You see on BTC-E a list of Buy orders and Sell orders, this is just guys like you. BTC-E is just a link between you and them.
If you don't want to buy fee you have to find people directly that are ready to sell LTC ;) (or find an exchange platform that do not have fees like BC24 which is closed ATM but this is another story)
btc-e.com 0.2% Trading fee 0.5 LTC for withdrawing Litecoin
vircurex.com 0.5% Trading fee 0.1 LTC for withdrawing Litecoin
these trading fee's are very low although i do admit the withdrawal fee's are high for any small transfers.
But really these are your only options and it's very unlikely any alternatives are around or will be around soon that can beat either.