Serendipity means a "happy accident" or "pleasant surprise"; specifically, the accident of finding something good or useful while not specifically searching for it.
These definitions are provided by Wikipedia.
Does this mean that you can sit around all day like a spiritual icon and expect the world to deliver all your wishes to you? I don't think so.
What is missing from the definition of the LoA is action.
Action is a critical component of the LoA. Not only must you focus on achieving certain goals, you must also take actions towards these goals. The Law of Attraction focuses on the thinking part to point out that your thinking can have conscious and unconscious impact on the actions that you take. The LoA does not prevent or restrict you from taking any and all actions in order to produce what you are thinking about.
A great example I just read was to image you want to test the LoA by imagining a purple feather showing up in your environment in the next 24 hours. If you are expecting to use serendipity instead of the LoA then you would just continue with your day as usual and see if a purple feather shows up somewhere. This would also be trying to see of the LoA had triggered your reticular activator such that you will notice a purple feather that you would not have noticed before.
Instead of trying to rely on the world providing your purple feather, a more probably success method would be to seek out the purple feather. How about performing a Google image search for a purple feather? How about visiting the local zoo or some other place that has peacocks or other birds that might have blue feathers.
There is the old saying "Genius is 1% inspiration and 99% perspiration". I don't know what the percentages are for the LoA in relation to thought and action, though I suspect many people assume it is something like 99% thought and 1% action. More likely, it is something like 20% thought, 80% action.
That 20% thought can be quite powerful and influence much of your actions so I don't at all discount that 20%. Just don't get deceived into believing that the LoA means sitting around thinking to yourself about how to achieve your goals.
Take action, now, to achieve your goals.