It was an invitation to be interviewed on the subject of the death of parents. But, as has been noted, both parents are still alive. As such, you wouldn't qualify to accept the literal invitation. Rather than invite the researcher to lunch, why not express interest in the study itself - find out more about it, ask for a reference reading or two, or something like that. Follow the clues.
Synchronicities are very subtle mysteries sometimes.
It was an invitation to be interviewed on the subject of the death of parents. But, as has been noted, both parents are still alive. As such, you wouldn't qualify to accept the literal invitation. Rather than invite the researcher to lunch, why not express interest in the study itself - find out more about it, ask for a reference reading or two, or something like that. The researcher is a religious person and saw this as a sign from on high that there are people out there that would be good subjects for this study even though, to this point, they have been very difficult to find.