Nothing really. Because of the way Duolingo is set up it treats the nikkud like accent marks in other languages, but unlike other languages like Spanish or German where omission of the accent amounts to a spelling mistake, omission of the nikkud is the order of the day. However, some sentences keep them in, to emphasize a pronounciation difference between what would otherwise be identical words.
In essence, there isn't much you can do, aside from quietly accept it as a quirk of Duolingo's engine.
The meaning of לך is actually "to you," as in "I am giving it to you, since the prefix "ל" means "to." יש לך literally translates as "there is to you," but since it isn't correct grammar to say that in English, we translate it as "you have." The possessive sentences make much more sense if you think about it this way. For example, ליונה יש מים is "to the dove, there is water," or "the dove has water." Hope this helps!