As for กัน in แล้วกัน, we don't have the actual meaning of กัน in แล้วกัน. We just use it together. Don't separate it because it will change the meaning of the sentence. We use แล้วกัน in some situation like this. Q1:ไปไหนดี (Where should we go?) A1: ไปพัทยาแล้วกัน (Pattaya) Q2: กินอะไรดี (What should we/I eat) A2: Noodles (กินก๋วยเตี๋ยวแล้วกัน) It's kind of used to answer questions that are asked for your opinion in order to suggest your idea. We use แล้วกัน in this case.

we use กัน when you invite someone to do something. For example, let's have lunch (ไปกินข้าวเที่ยงกัน). But sometimes, there is meaningless. we just say it. I don't know actually why. For example, why don't you guys have lunch? (ทำไมไม่กินข้าวเที่ยงกันล่ะ). You can notice i omit the subject. Also, you can omit the word กัน as well because it will not change the meaning of the sentence.

Hi!! แล้วกัน sometimes it might means" instead" and กัน in this, well it hard to say when separate it. It's just like we end with กัน to make sentence more smoothly

and together