Before we confuse serendipity with luck, please note that it is not just random luck but it is luck with a meaning. It is luck that happens at the right time that when you look back on it, you see that it was meaningful and leading to somewhere, in my estimation, somewhere always better than where you have been, either physically, financially, emotionally and otherwise.
I am however able to relate this with luck favours the brave or in more specifically a seeker rather than a lazy one. It means luck is not a 100% fate-driven but involves some efforts as well.
We assume luck is something like that will knock our door when we are sleeping.
Instead of being asleep, we assume buying a lottery (for example) is enough effort to be lucky. (Gambling is up to this).
But, serendipity is like buying a lottery ticket for every round or like buying 25% or 50% of total ticket in a round to be lucky. Some efforts rather than believing into complete fate.
Serendipity is all about not being complete random but maximizing the chances by some efforts IMO.