Aaron's troubles and the reason why he lied begins when Moses leaves to receive the Ten Commandments directly from the Lord.
Background
The children of Israel begin to panic when Moses tarries far longer on Mt. Sinai than they expected. Their remedy to ease their fears was to demand that Aaron, who was left in charge (Exodus 24:14), make them an idol to lead them (Exodus 32:1). Aaron immediately acquiesces to their demand without warning them that what they wanted to do was a great sin against God (Exodus 20:2 - 5).
The people, a short time after gold is collected from them, begin to joyously worship and celebrate around a golden idol. As a side note, this calf or ox shaped idol was likely Apis, the first and most popular pagan god worshipped by the Egyptians.
God soon informs Moses about the sinful behavior happening at the foot of Sinai (Exodus 32:7 - 8). After he hurries down the mountain he confronts his brother Aaron regarding the great sin he knowingly allowed the Israelites to indulge in (Exodus 32:21). What was Aaron's response, a man who is in his 80s, to his brother Moses?
Aaron's Excuse
Aaron admits asking the people for gold and then proclaims a bold lie, "So they brought them to me (gold jewelry, etc.) and I threw them into the fire, and . . . well . . . this calf came out!" (Exodus 32:24, TLB).
Aaron's attempt to dodge his inability to stand up for what is right, and his active role in angering God, is both sad and remarkably humorous.
At face value, he would have us believe that he innocently threw gold into a hot fire and, to his surprise, a large, incredibly heavy and fully formed pure gold image of Egypt's primary deity sprang out! What an amazing coincidence this magic occurred right at the time the Israelites wanted to pursue "mischief" (Exodus 32:22)! Aaron's unstated conclusion in his lie is that, once the idol "miraculously" appeared, it was only reasonable to allow it to be worshipped.
Missing Information
There is, of course, a great deal missing from Aaron's explanation that would have admitted choices, not magic, brought the idol into existence.
Aaron failed to state that he offered no resistance whatsoever to its creation (Exodus 32:2). Even worse, he did not admit that he supervised the creation of the idol's mold and the pouring of the gold into the rough cast. As if that were not enough, he personally refined and detailed, with engraving tools, the image (verse 4). Lastly, He leaves off the fact that he built the idol's altar (verse 5)!
Although we can find plenty of humor in the golden calf incident, at the time it transpired both the Lord and Moses were furious. God wanted to destroy both Israel and Aaron for their open idolatry (Exodus 32:9 - 10, Deuteronomy 9:18, 20). Even though Moses intervened to spare the people (Exodus 32:11 - 14), he soon destroyed the first copy of the commandments when he saw Israel's debauchery himself (verse 19).