Okay, I scoured the web trying to find answers, but had no luck. After a bit of lateral thinking I have found a solution for you…
Select all of your Line 1 Lyrics (on Mac I click on the first syllable of the line and press shift-cmd-A). Then open the Inspector (right click on the lyric text and select Inspector). Then uncheck the "2" box under "Play on pass:" (which is itself under "Playback"). To be absolutely safe, you could uncheck all except the "1" box, but this seems like overkill.
This seemed to work fine when I Exported as MIDI and then reopened in Sibelius. It's worth noting that you can also Export as MusicXML files, depending upon which program you want to open the file in. And, of course, an absolutely safe way to get around these problems is to simply enter music with no repeats, but instead written out in full!
Thanks to @Wheat Williams for Sibelius forum advice.