In Lev 24:11-23, we read the following:
The son of the Israelite woman pronounced the Name in blasphemy, and he was brought to Moses -- now his mother's name was Shelomith daughter of Dibri of the tribe of Dan--and he was placed in custody, until the decision of the Lord should be made clear to them. And the Lord spoke to Moses, saying: Take the blasphemer outside the camp; and let all who were within hearing lay their hands upon his head, and let the whole community stone him. And to the Israelite people speak thus: Anyone who blasphemes his God shall bear his guilt; if he also pronounces the name Lord, he shall be put to death. The whole community shall stone him; stranger or citizen, if he has thus pronounced the Name, he shall be put to death. If anyone kills any human being, he shall be put to death. One who kills a beast shall make restitution for it: life for life. If anyone maims his fellow, as he has done so shall it be done to him: fracture for fracture, eye for eye, tooth for tooth. The injury he inflicted on another shall be inflicted on him. One who kills a beast shall make restitution for it; but one who kills a human being shall be put to death. You shall have one standard for stranger and citizen alike: for I the Lord am your God. Moses spoke thus to the Israelites. And they took the blasphemer outside the camp and pelted him with stones. The Israelites did as the Lord had commanded Moses. (1985 JPS Tanakh)
In this narrative, the Israelites had to wait on special revelation given to Moses to give them instruction as to how to act with the son of the Israelite woman who committed an act of blasphemy; they did not view whatever scripture they had as being formally sufficient. Indeed, this incident and its implications for the doctrine of Sola Scriptura is mirrored by the narrative in Num 15:32-36, where we read a story of a man caught picking up sticks on the Sabbath.
What I wrote in my essay Not by Scripture Alone: A Latter-day Saint Refutation of Sola Scriptura on the pericope in Numbers is apropos for the Leviticus text, too:
What did they do? Did they dispute over the written records they had in their possession and from different denominations, with each one emphasising certain texts over other texts, as one finds in much of Protestantism (compare the debates between Reformed and free-will Baptists, for instance)? No, instead, God, through his divinely appointed spokesman, Moses, gave an explicit revelation on this issue, that that "fine-tuned," if you will, the pre-existing revelation on this matter, namely that it was illegal to pick up sticks on the Sabbath, resulting in this man being stoned.
On the offense of the man, the following note from Baruch J. Schwartz is insightful, showing that one had to be cognizant of the intentions of the man, and not just the act, further emphasising the need for special revelation:
11: Pronounced the Name in blasphemy: Merely uttering “YHVH” is not a crime in P; throughout the Bible this is a normal and even commendable action. Nor is uttering God’s name in falsehood or “in vain,” though prohibited in the Decalogue (Exod. 20.7 || Deut. 5.11), a case of blasphemy. Blasphemy consists of cursing God (see Exod. 22.27 and n.; 1 Kings 21.10-13), that is, uttering an imprecation against Him in which His name is included (“May such-and-such befall YHVH”). As the divine Name is one sacred “object” that can be used, or misused by anyone at any time (see 5.20-26 n.), it is only logical that in the Holiness Legislation this is a sacrilege par excellence. (The Jewish Study Bible, eds. Adele Berlin and Marc Zvi Brettler [2d ed.; Oxford: Oxford University Press, 2014, 255)