How would introduce Lois Lane in her first scene in Super Girl?

If they go traditional, she will undoubtedly be doing some dangerous investigative reporting and have to be saved from certain death (maybe a plane crash, since that seems to be a running theme throughout the various film and tv Kryptonian depictions).

And, since it's her show, Kara will undoubtedly do the saving.

""What, Clark was too busy; so he asked you to sub for him?"

Technically I think we’re going to see Lois on Flash first since that show gonna have the first installment. Why does there have to be any drama. Why not simply have Kara introduce her cousin and his girlfriend to everyone else. Let the drama come from the introduction of Batwoman not characters who aren’t potentially getting their own show.