There is a character, an older male, in this manga that I'm reading who uses this phrase twice
しないとな and the two lines are like this：
The first line, he is referring to himself (I should show my gratitude)-->I understood it more like "It wouldn't do if I don't show my gratitude" "I have/must...(among these ideas). It was more clear when the character said his 2nd line which I interpreted as: Say your goodbyes/Say farewell (note, he was directing this to another character that was with him).
I hope I made sense...What exactly is the usage of と here? What does it express? And does the 1st line sound okay with the interpretations I gave?