A negative question can be used to invite someone to do something together with the speaker. いいですね。～ましょう is a commonly used expression to accept the invitation.
(いっしょに) 食事を しませんか。
Would you like to have a meal with me/us?
(いっしょに) 映画を 見に 行きませんか。
Would you like to go see a movie with me/us?
A: (いっしょに) 行きませんか。
Won't you come with me/us?
B: いいですね。行きましょう。
That's a good idea. Let's go.
Lesson 4-8「いっしょに あの 店へ 行きましょう。」
Let's go to that store together.
Lesson 9-6「アリさんは いませんか。」
Isn't Ali there?
Lesson 9-6「はい、いません。」
No, he isn't here.