Extreme luck is more of a curse then a power, as while having extremely good luck sometimes can make your life different, extremely bad luck can basically flat out end it, or end you in a situation where even extremly good luck only goes so far (jail for instance).`
Good luck as a power would have to be like that chick in Deadpool, you basically have it all the time, and, yeah, depending on the level of the luck it could be insane....like jump off the top of a 20 story building and somehow luck makes you land without a scratch level of luck lol. Always win any games of chance, always have the odds in your favor, win anything you try at etc.
Pretty much you would never get sick either, so you would probably live without any illness till a very old age (probably longer then any other human before you), though you wouldn't be naturally immortal, if the technology was developed to make someone immortal, you would probably be lucky enough to get it lol.
I don't see how any of what you mention is a curse. ---