Lily walked in the forest with great caution for fear that she might be attacked by a/the giant snake. 

Lijy walked cautiously in the forest so that she should not be attacked by  the/a giant snake. 

Lily walked very carefully in the forest in case a/the giant snake might attack her.

小心翼翼可译为very carefully, cautiously, with geat caution等。在森林里走着，而不是走过森林，因此介词用in而不用through。之所以要小心，是怕被蛇咬，因此以防被蛇咬译成目的状语从句。可用in case, for fear that, lest, so that...not, in order that...not. 根据这个句子的语境和语体，用for fear that最为合适，介于正式与非正式之间。目的状语从句需要用虚拟语气，因此情态动词might不可缺少。目的状语不能用逗号。一条毒蛇不再大小，不大的毒蛇足以让人致命。这里要求用giant描述这条蛇，很可能是前面已经提及这条大蛇栖息在这个森林里。因此giant snake似应为特指。但这带有猜测的成分，故泛指也有可能。

被蛇咬，不一定要用bite，用attack更好一些。主句的主语为she，目的状语从句最好用被动语态，保持主语一致，不换主题。

供网友参考。