Shortly, it should end with dama not fatha, but in this case, when there is a "ي" before the pronoun "ه", we change it to kasra.

الهاء ضمير مبني على الكسر في محل جر مضاف اليه. تبنى على الضم في الأصل وتبنى على الكسر إذا سبقت بياء

There are some other words have the same rule as "لديه" has, like "عليه".

For me, it's not necessary to know all that. You just have to practice and to listen to the language and you will know automatically when to use dama or fatha or kasra without understanding these complex grammar rules.