Why 早 in "good morning" is read as HA-YO but no such reading of that kanji is in a dictionary?

Question

I see お早うございます in a dictionary also being written as おはようございます but why is 早 even there if it's read as HA-YA, not HA-YO? How do they know how to morph readings of kanji in a phrase into something else if it's not in the dictionary?