"남자가 자동차를 잠가요."
Translation:The man locks the car.
So here's my understanding (and somebody correct me if I'm wrong):
By right 으 should take 어요, but it's a weak vowel, so it always disappears. So instead you remove it and add 아요 or 어요 depending on vowel harmony with the next last vowel. In the case of 잠그다, the next last vowel after you remove the 으 is 아, so you add 아요.
To give another example, 짓다 which has the root modified to 지으 (Tips and notes - ㅅ special case) would then end in 이, so you add 어요. Hence 지어요.
If the root has only one syllable and there is no other vowel except the 으, go with 어요. So 크다 goes to 커요.