I think that it's quite intriguing how Desmond can now predict the future, because if it turns out that one can alter the future it eliminates the possibility of a pre-determined 'destiny', yet Desmond and indeed many other people on the Island believed that it was fate/destiny that brought them to the Island.

So it depends on whether Desmond 'saw' Claire getting struck by lightning or whether he saw himself prevent it from happening, because if he saw them get struck by lightning, he must have altered what he had seen, by constructing a lightning conductor. But if he saw himself prevent the lightning strike, then he is simply fufilling his destiny.

Relating this to whether he saw Eko die or not, that too would depend on how he sees the future. If he see's a pre-determined fate then he would have known that there would be nothing he or anyone else could have done for Eko.
However, if he sees an indeterminate future (one that may be altered by decisions and events) then he would have known that perhaps Eko could have been saved.

Perhaps the little details behind his apparent precognitive capabilities will be made clear to us later on in the season.