This is a difficult question to answer because every situation is different. Ask yourself what your motivation is in not loaning the money. Is it greed, fear of the future, lack of trust in your family member, or selfishness? If it is any of those things, you need to pray diligently for the Holy Spirit to guide you away from sin.
The Bible bluntly says, “If anyone does not provide for his relatives, and especially for his immediate family, he has denied the faith and is worse than an unbeliever” (1 Timothy 5:8). First, provide for your immediate family and then expand the scope of your generosity to include others. Your money should never be more important to you than helping others. We are specifically warned, “the love of money is a root of all kinds of evil” (1 Timothy 6:10).
If you are in a situation in which your family member has abused the generosity of family members in the past, and is untrustworthy, then you may truly be justified in not loaning the money. All you can do is pray that the Lord will show you His will and reveal the true motives of your heart.
“But whoso hath this world’s good, and seeth his brother have need, and shutteth up his bowels of compassion from his, how dwelleth the love of God in him?” (1 John 3:17)
“He that giveth unto the poor shall not lack: but he that hideth his eyes shall have many a curse” (Proverbs 28:27).
“He that tilleth his land shall have plenty of bread: but he that followeth after vain persons shall have poverty enough” (Proverbs 28: 19).
“He that hasteth to be rich hath an evil eye, and considereth not that poverty shall come upon him” (Proverbs 28:22).