Seven's luck association didn't start with numerology. Ancient astronomers tracked seven visible moving lights in the sky; several religious traditions treat seven as a marker of completeness; and "lucky number seven" shows up in English-language idiom well outside any numerology context, from dice games to slot machines.
Numerology, as a relatively modern system, mostly inherited that pre-existing reputation rather than building it from scratch. When a birth date reduces to 7, the tradition folds the older cultural symbolism into its reading of that birthday number.