Learn Finnish: Jos koira ei lakkaa haukkumasta, naapuri suuttuu. - If the dog does not stop barking, the neighbor will get angry.

The verb lakata (to stop or cease) requires the action you are stopping to be in the third infinitive elative form, which ends in -masta or -mästä. You can think of it as stopping from doing something: "The dog does not stop from barking."

Why does the verb lakata have a double 'k' in ei lakkaa?

Lakata is a Type 4 verb. These verbs undergo reverse consonant gradation, meaning the weak consonant in the infinitive (a single k) becomes a strong consonant (a double kk) in the conjugated forms, including the present negative ei lakkaa.

Could I use the verb lopettaa (to stop) instead of lakata here?

You could, but it changes the grammar. While lakata requires the -masta form (lakkaa haukkumasta), lopettaa requires a verbal noun in the partitive case, which ends in -mista. So you would say ei lopeta haukkumista. They mean the same thing but demand different grammatical rules.

The English translation says "will get angry", but isn't suuttuu in the present tense?

Yes, it is! Finnish does not have a separate future tense. You just use the present tense for future actions. The conditional context of the sentence (the "if" clause) makes it perfectly clear that the neighbor getting angry is a consequence that will happen in the future.