Should I include a cover letter after asked to interview?

If they asked for an updated Resume, I would include a cover letter as a matter of course.

Even if you have the Interview in hand.

If you are posting it or emailing it then a cover letter is required so the other person knows what it is about.

And even if you are handing it over in person, it is polite to include a cover letter. It is also prudent - that person could forward your resume to someone else, who then needs to the reason for it, or the background.

If a cover letter is customary in your locality, you should include one.

Getting directly invited to join the pool of candidates may give you a slight leg up, but otherwise they clearly still intend to follow the normal hiring process with you, so treat it that way. A good topical cover letter can help show them that you're taking this opportunity seriously and not expecting any preferential treatment.

In general, in localities where cover letters are customary, not including one can be seen as rude, brusque, or even entitled, regardless of how much of a shoe-in you are for the position. Just also be aware that in localities where they are not customary, including one can hurt your chances, since they can be seen as overly formal and it can look like you don't know the locality you're applying in well enough to know cover letters are not commonly used there.