(Spoiler Alert) Can anyone help with a movie time travel paradox?

End of Movie Spoiler Alert

Ok so we just watched the movie “The Lake House” Where the characters Kate and Alex converse through time (2 year difference, Kate being in 2006, and Alex in 2004) through a mailbox at the lake house.

At the end of the movie Kate is in 2008 and Alex is in 2006…. Yes I know it’s a movie but this part is really confusing….

Kate writes to Alex in one letter that because a man died on Valentine’s Day 2006, his death is what brought her back to the lake house, and therefore, when she found Alex’s first letter. However, when Kate realizes in 2008 that Alex was that same man who died on Valentine’s Day (2006) from his brother she hired to renovate her current house, she warns him not to find her in order to save his life, and for him to find her at the lake house in another 2 years. Alex doesn’t die, and he does meet Kate.

So if he didn’t die on Valentines Day (2006), She wouldn’t have returned to the Lake House and find his first letter….She also wouldn’t of found out from his brother that he has died (the cause of her wanting to save his life) and be able to warn him not to show up when he did… So wouldn’t he need to die for this to work….? uggg headache