Can someone tell me how to say this in Korean?
Can someone please tell me how to say "I'm gonna meet one of my friends soon to have lunch together. What are you doing?/How about you?" in polite speech?

Question

Answer

Polite way

저는 오늘 친구랑 같이 밥 먹으려고요. Name씨는 이따 뭐하세요? 
Or 
저는 오늘 친구만나서 같이 점심/밥 먹으려고요. Name씨는 이따 뭐하세요?

With friends or close someone

(나는) 오늘 친구랑 같이 밥먹으려고. 너는?
Or 
(나는) 오늘 친구만나서 같이 점심/밥 먹게.
너는?