I don't think Paolini was lucky. If I remember correctly he and his family put a lot of effort into self publishing and promoting the first book before self publishing was cool or easy. He went to a bunch of schools and libraries to promote it.
I guess there was some luck since according to Wikipedia the stepson of an author found it and liked it, and his dad ended up pitching it to his publisher, who picked up the series. But it looks like it took a lot of work to make the luck happen.