Learn Spanish (Latin America): No me gusta dilatar la pupila.

No, it actually means the speaker is the one doing the dilating! Because it uses the infinitive dilatar directly after me gusta, the speaker is the subject of both verbs (perhaps they are an eye doctor). To say "I don't like having my pupils dilated," you need a change of subject and the subjunctive: No me gusta que me dilaten la pupila.

Why does the sentence use la pupila instead of a possessive like mi pupila or su pupila?

As a quick refresher: in Spanish, body parts almost always take definite articles (el, la, los, las) instead of possessive adjectives (mi, tu, su) as long as the "owner" of the body part is obvious from the context.

Is dilatar only used for medical things like pupils?

While it literally means "to dilate" or "to expand" physically, in many parts of Latin America (especially Mexico and Central America), dilatar is also a very common conversational verb meaning "to take a long time" or "to delay." For example, someone might say No me dilato to mean "I won't take long."

How could I use this lesson's grammar point (lo + adjective) to say "The annoying thing is dilating the pupil"?