Hi Lance,
How exciting that you are looking into the parents of your great-grandfather. I know it can be hard to find out more about ancestors sometimes, but I'm happy to give you some guidance.
Can you say what you've done so far to find out more about John Navin's parents? Where did you look for information? Did you already look into Irish archives with the idea that they might have been born on the island, or did you do research in your local US registry office and archives?
If his parents were born on the island of Ireland, you can use
this resource on starting your Genealogy journey to continue your research. It's important to know when and where they were born to know where to look. Your best bet to find out is by looking for their death certificates in the US. If they passed in the US but were born in Ireland, it's time to reach out to the appropriate records office in Ireland.
Leget is not a name that comes up in a mid-nineteenth century Ireland surname search, but
there are some variant spellings that might be a better match.
I hope this helps! Good luck with your research!
Noortje