Without considerations of the overall story, would there be a reason why the text would need to be interpreted with one or the other of these two groupings of genitives, or could either be okay. In other words, are their constraints on Greek usage here, rather than only context, that the authour could safely assume his readers would emply as they decoded the meaning of this part of the text?καθήμενοι δὲ περὶ τῆς Μυρτάλης καὶ τοῦ Λάμωνος ἐπυνθάνοντο καὶ εὐδαιμόνιζον αὐτοὺς τοιούτου γηροτρόφου εὐτυχήσαντας.
Which is possible?
Either:
καθήμενοι δὲ περὶ τῆς Μυρτάλης "Sitting around M"
καὶ τοῦ Λάμωνος ἐπυνθάνοντο "they both made enquiries about L"
καὶ εὐδαιμόνιζον αὐτοὺς τοιούτου γηροτρόφου εὐτυχήσαντας. "and considered them blessed because ..."
And / or:
καθήμενοι δὲ περὶ τῆς Μυρτάλης καὶ τοῦ Λάμωνος "sitting around M and L"
ἐπυνθάνοντο καὶ εὐδαιμόνιζον αὐτοὺς τοιούτου γηροτρόφου εὐτυχήσαντας. "they made enquiries and considered them blessed because ..."