Hi Dragana, you are actually confusing 2 different types of pronouns.
The lesson you refer to is actually about indirect object pronouns. ( me-te-lui-nous-vous-leur ) "leur" in this case means them or to them and it doesn't need an 's' as it is already a plural, "lui" can be used for a man or a woman and means him /her or to him/ to her.
There is another type of pronouns called Possessive Pronouns which will be covered by another lesson and there is a "leur" ( singular) and a "leurs" ( plural ) to translate "their ".
e.g. C'est leur frère , c'est leur mère , ( It is their brother, their mother) , Ce sont leurs frères ( These are their brothers) , Ce sont leurs affaires, ( These are their things ).
The "leur", "leurs" here agree ( singular or plural ) with the noun they refer to.
Hope this helps!