"I believe lions don't eat vegetarians."
Translation:Ich glaube, Löwen essen keine Vegetarier.
You may perfectly write "Ich glaube, dass Löwen keine Vegetarier essen", an equivalent to the explicite "that lions don't eat vegetarians", but notice you have then to put the verb at the end of the clause. Duo's version is an alternative possibility, where you skip the subordinate conjunction and keep the verb in second position. Just stylistic choice here :)
Curious, I wrote "fressen" just now, and it was accepted, although Duo suggested another translation using "essen". My construction was..".dass.....fressen", but that surely doesn't matter. It all suggests that "Leute essen Tiere, und Tiere essen Leute, aber Tiere fressen andere Essen."?
Normaly the algorithm is indifferent to punctuation.
While I am not contributing to this course, I simply assume the author of this sentence wanted to somewhat "humanize" the lions.
If "fressen" is indeed not accepted, please report, I'm very sure someone will correct it sooner or later.