I am playing Swiftblade and she has the ability lucky, I just got the companion Travel Guide and it says if I ever roll a 1 on a survival roll the companion leaves but I have the skill lucky.  So if I ever roll a 1 I get a re-roll, so would the companion stay?

Yes, if you roll a 1, you get to reroll and thus negate that 1. The Travel guide stays.
However, if your second reroll is also a 1, you must keep it. Then the Travel guide would leave.