Since there isn't any connection to a market that trades litecoins to balance out the price variation - you could have a rule that says your site wouldn't trade (or at least won't force liquidate)  litecoins at some level - like 50% below or 100% above of the market price (getting an average market price from other sites).  Or even a narrower band (though I wouldn't go narrower than 10-30%).

This makes sense especially as Bitfinex isn't a market-maker or leader in litecoin.