What is the biblical basis against the idea of luck?

To the committed believer who rests upon God's love, there is no such thing as luck. As the passage says, "And we know that all things work together for good to those who love God, to those who are the called according to His purpose" (Romans 8:28).

To the one who has finally believed that God really takes care of him or her, there is no such thing as luck; God uses both the good and bad for the good of the individual. From the carnal standpoint, we would see unlucky happenings as undesireable things happening to us, but for the one who is convinced that God loves him, those event are allowed by God for some reason, such as to train him up in character, like teaching him patience. They are neither lucky nor unlucky incidents, but guided by God for good.

So the idea of luck, whether good or bad, depends on the perspective of the person's relationship with a loving God, according to Romans 8:28.

James says

If a brother or sister has nothing to wear and has no food for the day, and one of you says to them, “Go in peace, keep warm, and eat well,” but you do not give them the necessities of the body, what good is it?

James 2:15-16 NABRE

which I thought I recalled being translated, "good luck, see ya later, hope you don't starve to death and die of exposure!" But still has the same connotation as wishing someone luck while not providing for their needs.

Clearly depending on luck is a bad idea and having an expectation of good fortune for others when you could be providing form them rather than merely wishing them good luck is useless, and is not true faith.

You may be surprised but there is no such thing as "luck" for Christians. As the other nations believe that if one has a good luck, whatever one does, he always wins, or if one has a bad luck, whatever one strives to make good, he always fails, but sadly this is the world view or pagan view which leaves no choice to anybody whereas the Bible clearly states in Deuteronomy 11:27-29 about how to receive BLESSING OR CURSE. The choice is ours. If we start accepting the pagan view, it leaves no choice to luck believers.

For us the commandment is not to indulge or adopt the teachings of any other nation.

In both the Old and the New Testaments, drawing of lots is used as a means of discerning the will of God - he controls events that appear random to us.

The Urim and Thummim were (probably) two objects kept inside the clothing of the high priest, who would draw one out "at random" to get a yes-or-no answer to some question. This happens, for example, in 1 Samuel 14 to see who had broken Saul's order not to eat any food on a particular day; here are verses 40-42 in the NIV:

Saul then said to all the Israelites, "You stand over there; I and Jonathan my son will stand over here."

"Do what seems best to you," they replied.

Then Saul prayed to the LORD, the God of Israel, "Why have you not answered your servant today? If the fault is in me or my son Jonathan, respond with Urim, but if the men of Israel are at fault, respond with Thummim." Jonathan and Saul were taken by lot, and the men were cleared. Saul said, "Cast the lot between me and Jonathan my son." And Jonathan was taken.

The part I have put in italics above is in the Greek version (the Septuagint) but not in the Hebrew.

In the New Testament, the disciples draw lots to determine who is to succeed Judas. This happens in Acts 1:23-26:

So they nominated two men: Joseph called Barsabbas (also known as Justus) and Matthias. Then they prayed, "Lord, you know everyone’s heart. Show us which of these two you have chosen to take over this apostolic ministry, which Judas left to go where he belongs." Then they cast lots, and the lot fell to Matthias; so he was added to the eleven apostles.