You can use present simple closes about a general truth (something that always happens) or about a scheduled event
Ice melts if you heat it - general truth
My flight leaves at 9:45 - scheduled event.
You can use present continuous be closing about something that is happening right now, or something that is planned or intended to happen soon.
I am writing a book - right now
I am leaving tomorrow - intent
You can use be going to infinitive for something that will happen or intended to happen: usually it means soon, but could be some time away.
There is going to be a full moon tonight - will happen
I am going to make dinner soon - intent
We are all going to die one day - will happen eventually
You can also use will infinitive for something that will definitely happen or you intend to happen at any time in the future.
The sun will rise at 5:43am - will happen
I will go to America one day - intent
All of the versions that you have suggested would be OK, but the best would be
Let's walk quickly because the shop closes in ten minutes. - scheduled
Let's walk quickly because the shop is going to close in ten minutes. - will happen soon
Let's walk quickly because the shop will close in ten minutes. - will definitely happen
These three examples are all equally good: the circumstances might affect which one you choose to use. is going to close is slightly less formal. There is not much difference between the other two, unless you want to distinguish between scheduled and will definitely happen.
The weakest is this version, because it's not happening now and it's not something that you plan or intend.
Let's walk quickly because the shop is closing in ten minutes