Is there such a thing, do we have a measure of randomness and ability to shape our own destinies or ultimately are all things predestined.
I'll give you one perpective. According to the following verse:
Romans 8:28 (ESV)
And we know that for those who love God all things work together for good,fn for those who are called according to his purpose.
In other words, to the Christian who has grown to love and trust God implicitly, God's hand is in everything in his life, in both good and "bad" events. Even the negative circumstances are taken as though from God, allowed by God to shape the believer's character, as it states in Romans 5:3-4,
Not only that, but we rejoice in our sufferings, knowing that suffering produces endurance, and endurance produces character, and character produces hope,
You may be confusing luck and shaping our own destinies. They are not mutually exclusive. If I want to lose 10 lbs, I can trust to chance or make my own luck by eating fewer calories than I burn until I get the weight I want. But when I act on it, then, according to the dictionary of English words, the event is no longer luck, but a planned event. If you plan something to happen, then it is no longer luck. (This is not always correct though: you can intentionally make your way to a red-carpet gala to get a movie star's autograph (not luck) and either the star doesn't show up, or you're too far to get to him (bad luck.)
The Bible does not have any Scriptures on 'luck' per se , but does have several in which it talks about chance. The difference is that chance according to Webster is: An event that happens, falls out or takes place, without being contrived, intended, expected or foreseen; the effect of an unknown cause, or the unusual or unexpected effect of a known cause; accident; casualty; fortuitous event; as, time and chance happen to all.
Chance and luck can sometimes be interchangeable.
all Scripture is quoted from the King James translation.
In the following Scriptures you might use luck in place of chance.
1st Samuel 6:8 and 9
And take the ark of the LORD, and lay it upon the cart; and put the jewels of gold, which ye return him for a trespass offering, in a coffer by the side thereof; and send it away, that it may go. And see, if it goeth up by the way of his own coast to Bethshemesh, then he hath done us this great evil: but if not, then we shall know that it is not his hand that smote us: it was a chance that happened to us.
2nd Samuel 1:6
And the young man that told him said, As I happened by chance upon mount Gilboa, behold, Saul leaned upon his spear; and, lo, the chariots and horsemen followed hard after him.
I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.
but with this verse Chance and luck have different meanings.
The lot is cast into the lap; but the whole disposing thereof is of the LORD.
My concordance does not record the word luck as in the bible. Do we have an ability to shape our destiny? Yes. We have choice.
Deuteronomy 6;21 And the LORD commanded us to do all the statues, to fear the LORD our God, for our good, that he might preserve us alive, as it is at this day.
Proverbs 1;7 The fear of the LORD is the beginning of knowledge,; but fools despise wisdom and instruction.
Proverbs 28;26 He that trusteth in his own heart is a fool: but whoso walketh wisely shall be delivered.