Yes, luck (and bad luck) exists. As for why, I don't really know but my theory is that it's because of the way the world is designed. Firstly, the chances of life emerging into existence is extremely, extremely low yet it happened anyway due to DNA being able to self replicate. Pro lifers may consider this to be the luckiest thing ever but I bet that people here (me included) consider this to be the unluckiest thing ever. Secondly, if you put a bunch of organisms into a finite space with finite resources, you get competition. As in the case of all competitions, there will be winners and losers. As in the case of life, losing a competition could mean something as drastic as dying horrifically to a species higher up in the food chain.
Additionally, humans have created a bunch of arbitrary systems which has created even more luck within it. Those who are born into a rich family (an arbitrary concept made by humans) are considered lucky whereas those who are born into poverty are considered unlucky.
There's a lot of other things that determine somebody's luck in life due to all of the random shit that could happen. You could one day get your body all mangled up due to a car accident or you could get cancer or you could be born with a disability and the list of the bad things that could happen is endless.
I also somewhat believe that luck requires an element of comparison to it. If everybody was the same from birth to death with no deviations in anything, could any of them really be considered as lucky? I think that we need to be lucky or unlucky with respect to something. In my case, I'm unlucky because I was born with a flawed neurotype whilst most people have a normal neurotype. In my case, I'm suicidal and crave death just like a lot of people on here yet I'm trapped in existence and forced to stay alive until natural death whereas most people here are able to escape existence. I'm unlucky relative to those who are more lucky (or less unlucky depending on how you view it)