Because people are so obviously unequal in so many ways, it is tricky saying what one means by saying everyone is "equal before the law." Putting a high value on freedom makes that easier, because then "equality before the law" means that everyone gets to do whatever they want in as long as they respect other people's right to do whatever they want. I discuss some of the complexities in this in "The Complexity of Liberty: How Equality Enters into a Good Definition of Liberty," but the basic idea has become intuitive in our society, which has a fairly well-defined notion of the boundaries of each person's private sphere.
The issues I discussed in "The Complexity of Liberty: How Equality Enters into a Good Definition of Liberty" were about setting the boundaries between the private spheres of different adults. After laying out how freedom provides a way of thinking about equality under the law in section 54 of his 2d Treatise on Government: “Of Civil Government” (Chapter VI. Of Paternal Power), in sections 55 and 56, John Locke deals with a different complication: limitations on the size of the private sphere of freedom for children. What John Locke emphasizes is that the limitations on children should be temporary ones.
Though I have said above, Chap. II. That all men by nature are equal, I cannot be supposed to understand all sorts of equality: age or virtue may give men a just precedency: excellency of parts and merit may place others above the common level: birth may subject some, and alliance or benefits others, to pay an observance to those to whom nature, gratitude, or other respects, may have made it due: and yet all this consists with the equality, which all men are in, in respect of jurisdiction or dominion one over another; which was the equality I there spoke of, as proper to the business in hand, being that equal right, that every man hath, to his natural freedom, without being subjected to the will or authority of any other man.
Children, I confess, are not born in this full state of equality, though they are born to it. Their parents have a sort of rule and jurisdiction over them, when they come into the world, and for some time after; but it is but a temporary one. The bonds of this subjection are like the swaddling clothes they art wrapt up in, and supported by, in the weakness of their infancy: age and reason, as they grow up, loosen them, till at length they drop quite off, and leave a man at his own free disposal.
Adam was created a perfect man, his body and mind in full possession of their strength and reason, and so was capable, from the first instant of his being, to provide for his own support and preservation, and govern his actions according to the dictates of the law of reason which God had implanted in him. From him the world is peopled with his descendants, who are all born infants, weak and helpless, without knowledge or understanding: but to supply the defects of this imperfect state, till the improvement of growth and age hath removed them, Adam and Eve, and after them all parents were, by the law of nature, under an obligation to preserve, nourish, and educate the children they had begotten; not as their own workmanship, but the workmanship of their own maker, the Almighty, to whom they were to be accountable for them.
In American society, we take it for granted than children are no longer subject to their parents after a certain age (typically 18), absent a serious mental disability. But not all societies have allowed children to be automatically emancipated from their parents at a certain age. I suspect that English society already allowed children to be emancipated after a certain age even in John Locke's time, so that John Locke could use that English custom to give a counterargument to the idea that the authority of monarchy could derive from the power of parents over their children.
For links to other John Locke posts, see these John Locke aggregator posts: