are the rich 'lucky'

if you consider luck being born rich, yes.

if you consider luck being born in a first world country, yes.

if you consider get a product/service stuck long enough to turn a profit, yes.

if you were born poor, if you were born in a third world shithole, your chances are nought.

if you create something worth buying/using, you need luck to keep your users. but it is likely some chink will produce your design and beat you manufacturing it (see the autism block that was on the news yesterday, or the selfie stick case). 
if you design a service or some game for example, you will have clones by the millions if it gets any attention, and it is likely a clone will rob your success (see candycrush)

buy lottery tickets. you have as much chance in getting rich if you are poor.