Keep the Fire Burning; Eye for an Eye
The lamps of the menorah were to be lit and kept burning every day (verse 2; Exodus 27:20 Exodus 27:20And you shall command the children of Israel, that they bring you pure oil olive beaten for the light, to cause the lamp to burn always.
American King James Version×; Exodus 30:7-8 Exodus 30:7-8  And Aaron shall burn thereon sweet incense every morning: when he dresses the lamps, he shall burn incense on it.  And when Aaron lights the lamps at even, he shall burn incense on it, a perpetual incense before the LORD throughout your generations.
American King James Version×). This was symbolic of God's Spirit and His laws. Each day, we must have the light of God burning in us through His Spirit and living by His Word. David prayed to God, "Your word is a lamp to my feet and a light to my path" (Psalms 119:105 Psalms 119:105Your word is a lamp to my feet, and a light to my path.
American King James Version×). Echoing this, Solomon wrote: "For the commandment is a lamp, and the law a light; reproofs and instruction are the way of life" (Proverbs 6:23 Proverbs 6:23For the commandment is a lamp; and the law is light; and reproofs of instruction are the way of life:
American King James Version×). When people see us, they should see God shining through us. "Let your light so shine before men, that they may see your good works and glorify your Father in heaven" (Matthew 5:16 Matthew 5:16Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven.
American King James Version×). Just as with the tabernacle lamps, this requires attentiveness and vigilance.
The phrase "from evening until morning indicates tending the lamps twice a day, not tending them throughout the night" (Nelson Study Bible, note on Leviticus 24:2-4 Leviticus 24:2-4  Command the children of Israel, that they bring to you pure oil olive beaten for the light, to cause the lamps to burn continually.
 Without the veil of the testimony, in the tabernacle of the congregation, shall Aaron order it from the evening to the morning before the LORD continually: it shall be a statute for ever in your generations.
 He shall order the lamps on the pure candlestick before the LORD continually.
American King James Version×). Similarly, we must seek God when we awake each day and before we go to sleep each night to make sure that our spiritual "oil" is renewed (compare Matthew 25:4 Matthew 25:4But the wise took oil in their vessels with their lamps.
American King James Version×; 2 Corinthians 4:16 2 Corinthians 4:16For which cause we faint not; but though our outward man perish, yet the inward man is renewed day by day.
American King James Version×)—allowing us to shine every day.
In verses 19-20 of Leviticus 24, we come to the "eye-for-an-eye" principle, mentioned earlier in Exodus 21:23-25 Exodus 21:23-25  And if any mischief follow, then you shall give life for life,
 Eye for eye, tooth for tooth, hand for hand, foot for foot,
 Burning for burning, wound for wound, stripe for stripe.
American King James Version×. We stated in our highlights on that passage that this was apparently not generally meant to be a literal requirement in meting out justice—that just recompense was the concern. The judges of Israel might have required death or beating with a certain number of stripes. And that would have been literal. But we have no evidence that the judges ever required a hand to be cut off or other bodily mutilation (although it is possible that they did since there is no way at present to really know).
It may be that they would allow the offended party to exact that penalty from someone who had cut his hand off (similar to God's allowance for the nearest of kin to a murder victim to act as an avenger of blood). As mentioned in the highlights for Exodus 21, a big reason for the principle was not just so that the punishment would fit the crime but so that the punishment would not go beyond the crime. The Nelson Study Bible notes on Leviticus 24:19-20 Leviticus 24:19-20  And if a man cause a blemish in his neighbor; as he has done, so shall it be done to him;
 Breach for breach, eye for eye, tooth for tooth: as he has caused a blemish in a man, so shall it be done to him again.
American King James Version×: "Its purpose was not to require the injured party to inflict equal bodily harm on the one who had injured him, but to forbid him from inflicting greater bodily harm."
Of course, while God's system may have allowed justice to be measured out in kind as described, His desire was for mercy in the face of remorse—and also for restitution and care for the victim. If someone cut another person's hand off, the person who lost his hand would be wiser to not cut the offender's hand off. The judges would perhaps order a beating for pain and suffering and that the offender work (maybe for the rest of his life) to provide the lost livelihood to the one who lost his hand and was no longer able to work. (If the offender's hand was cut off too, he could not work to help the victim. So it would not seem to really help matters—except in giving some sense of justice and providing a deterrent in the society.)
The same goes for blinding an offender if he has blinded someone else. This would create two needy beggars instead of just one. It seems wiser to demand that the seeing criminal be indebted and perhaps indentured to the victim.