The girl lost the dog. At least be consistent as to whether or not we can assume the possessive. Marking it right sometimes, and wrong others is just pointless.
The course is new. Both should be accepted so just use the flag whenever there is an issue. It's going to take time for the lessons to include all possible answers.
What about 잃었어요? I heard adding 버리다 carries a meaning of completeness, but could both work ?
Yes, both are fairly synonymous.
Is "여자아이가 그녀의 개를 잃어버렸어요." wrong? ....ㅠㅠ
This makes me feel sad.