grammar - Interpreting させていただきます

Speaker 1:先{さき}に食事{しょくじ}に行{い}っていいよ
Speaker 2:では,そうさせていただきます

Please help understand this conversation - especially the 'させていただきます' construct.
What would this translate into English as?

Answer

The form

The sentence, そうさせていただきます, is a typical example of use of 謙譲語{けんじょうご} (humble language).

Translation

Let's make the Speaker2's sentence a normal form. (Earlier step is politer.)

Step 1. では、そうさせていただきます。

Step 2. では、そうさせてもらいます。

Step 3. では、そうします。

Step 4. なら、そうする。

So, these sentences can be translated like:

Speaker1: You can go for a meal earlier than me.

Speaker2 (Literal): Well, I do so.

Speaker2 (Free): Well, I go.

Speaker1 allows Speaker2 to go for a meal earlier than Speaker1.

Then, Speaker2 responds to him.

(The translation on the meriororen's comment is not correct because Speaker2 has already been permitted to go when s/he responds.)

Reference: Kenjogo

Humble language, 謙譲語{けんじょうご}, is used when you talk to someone higher ranking than you.

Here is a great explanation: Business Japanese – Keigo II – Kenjougo Japanese Talk Online