Before I begin I feel like the general understanding of 3+ dimensional beings is that for them time is just another physical dimension. One of the comments mentioned that this entity can "simply walk from one point in time to another".
I beg to differ here. Please bear with me as this is related to answering the question.
You do realize that every time you walk to literally any place you're travelling in time right? You're not consciously travelling in time but you're essentially moving steadily forward along the axis of time all the time anyway. Now if time were a physical dimension, i.e. you can simply walk/climb/swim to the past or future, how is the time you spent walking/climbing/swimming accounted for? In other words, you're effectively moving along two time dimensions, one which you traverse as a physical dimension and the other you continue traversing as you do now.
I propose that a higher entity with the ability to exist in more than 3 dimensions must necessarily possess a cognitive ability to traverse time, not a physical one. Think Dr. Manhattan, not Interstellar.
EDIT: Pursuant to the comment made by User, I'm rejigging the answer to exclude a cognitive perception of all possible timelines and include a physical one. Though on really thinking about it, the final answer and explanation do not change much.
We have an entity that travels across time like a physical dimension. Now if such an entity were to encounter great luck or misfortune, I do not believe it would make any difference in terms of the entity taking cognizance of it.
If such an entity won the lottery, it would still consider itself lucky. My chances of winning a lottery are low, and it would be a great surprise if I won the lottery as a normal human being. As a higher entity, I may know I am bound to win the lottery, since I see myself winning it a few feet to the left or a mile down the line, whereby it would be no surprise to me, but I'd still be aware that it takes incredible luck to win something like that. I reckon I'd still feel grateful and lucky about it.
Luck, as Frostfyre points out, is independent of time. Probability on the other hand, is completely dependent on viewpoint which may be before or after a fact in time. Which brings me to the question of serendipity.
As defined by Webster Serendipity is "the faculty or phenomenon of finding valuable or agreeable things not sought for."
There appears to be an element of discovery to serendipity. It is not merely feeling lucky, it is feeling lucky in circumstances where it was not expected. And there, I believe, lies the answer. When you're a being incapable of being surprised, I don't think you can find anything "unexpected", thereby rendering you incapable of feeling this emotion altogether. My answer, in light of the above, is therefore no - a higher being capable of existing in all times at once cannot experience a serendipitous moment.
Unless you're saying it takes a long amount of time (the second time dimension) to traverse time (the first time dimension). In that case, discovery of time-related facts would be much akin to discovery of physical features when out on a drive in the plains. Since we're explicitly excluding precognition, this seems plausible.
In that case, yes, surprise, discovery and serendipity, are all possible. I could walk down to the future and discover something valuable in an unexpected place (though it is in the future), and that would be serendipitous as per the definition wouldn't it? Really, the crux of it is this: how much do these beings know about their future? Not what they can discover, but what they are already aware of. Not knowing at first is the key to serendipity IMHO.