The correct sentence is: "Let us go out for a walk."

The sentence uses the article "a" before the noun "walk." The article "a" is used to refer to one, any, or some of a thing or things not already known or specified.

In this case, "a walk" refers to a type of activity that involves walking. The article "a" is necessary to indicate that the speaker is suggesting going out for one particular type of activity, which is a walk.

The other options are incorrect because they do not use the correct article or noun form. "Let us go out for walk" is incorrect because it omits the article "a" before "walk." "Let us go out for a walking" is incorrect because "walking" is a gerund (a verb form ending in "-ing" that functions as a noun), but it needs an article to specify which walking activity is being referred to. "Let us go out for walking" is also incorrect because it uses the gerund form "walking" instead of the noun form "walk," and it lacks the necessary article