Let’s go swim.

Let’s go cook.

Let’s go run.

Let can function as a transitive verb OR as an imperative.

It can take an object, as in the above sentences where the infinitive or the participle can function as the object in most cases. It only makes sense for that object to be a present or past participle IF the process is physically active.

If you examine it, the infinitive makes more sense most of the time, and the “go” is not even neccessary.

Let’s swim. Let’s cook. Let’s hike. or even Let’s cook.

Adding “go” as an element of the sentence suggests leaving to do something.

Using the participle makes sense when it is a physical process, especially of exertion. Running, hiking, jogging.

Cooking is not a physical sport that requires “going” to, you can do it practically anywhere. It no more requires “going” than sleeping, reading, napping, snoring.

So I would suggest that you only put together “Let’s go…” plus the present participle of a very few select actions. If I were you, I would just memorize the correct ones.

Besides, you CAN say Let’s go cook. Let’s go read. Or even Let’s cook. Let’s read.

If you want more on “go” read the Oxford English Dictionary about it–It takes up something like 45 columns of fine print.

Where I’m from, we use it all the time, That is good ole country talking and it really don’t matter whether its good english or not, we just do it. I have heard my granny say a lot of time, Let’s go do some cooking, and when its done we will play!

But note, that you can tell someone in the living room to “go cook” but if you’re in the kitchen, “go cook” sounds odd.

go is an obvious choice for those things which are done outside the house.

go on a picnic

go to the movies (which isn’t said when watching at home)

go skiing

But I would have loved to go to breakfast. Maybe Go has become more descriptive than it used to be.