Why do Catholic laity cross themselves three times before the Gospel is read?

Having been a lifelong Catholic, I have only picked this up through seeing other people do it. That being said, I have always seen it as being symbolic of keeping the Gospel in my mind, on my lips, and in my heart.

You can find some other perspectives on it here and here.

Contrary to what you say about missals, the rubrics in my missal (The CTS New Daily Missal) say that before the reading of the gospel, "He [the deacon/priest] makes the Sign of the Cross on the book and, together with the people, on his forehead, lips, and breast." (emphasis added)

Why do Catholics sign themselves three (3) times just before the Gospel is read?

To understand the significance of this tradition, let us take a look into its origins.

Concerning the making the sign of the cross at the proclamation of the Holy Gospel, after the deacon or priest says, “A reading from the Holy Gospel according to ….,” he and the faithful make the sign of the cross with the thumb on the forehead, lips, and breast over the heart. (The deacon or priest also makes the sign of the cross on the Lectionary or Book of the Gospels.) The first recorded instance of making the sign of the cross at the proclamation of the gospel is found in the ninth century: Regimius of Auxerre (d. c. 908) in his Expositio recorded how the people in the congregation would sign their foreheads, and the deacon would sign his forehead and breast. By the eleventh century, as attested to by Pope Innocent III, the deacon would make the sign of the cross on the Lectionary or Book of Gospels, and then both he and the congregation would sign the forehead, lips, and breast. The significance of the threefold signing is that we want to hear the Holy Gospel with an open mind, proclaim it with our lips, and cherish and safeguard it in our hearts. We are imploring the Lord for the grace to receive, acknowledge, and then profess the faith that has been received in the Holy Gospel through our Lord, Jesus Christ, the Word of God incarnate. - Catholic Straight Answers.

Not everyone of the Roman Rite follows this tradition.

Carmelites do not make the three-fold sign of the cross on their forehead, mouth, and breast when saying the words "Gloria tibi, Domine" before the proclamation of the Gospel during Mass. The reasoning is that their rule predates the introduction of the gesture into the liturgy. - EWTN

There are Religious Orders that make a rather large sign of the cross, in lieu of three small ones just before the proclamation of the Gospel.

Before the Gospel is read, a Catholic makes signs of the cross, with the thumb, on his or her

1. forehead,
2. mouth, and
3. heart,

which represents that the Catholic must

1. understand the Gospel,
2. proclaim it, and
3. "take it to heart," i.e., put it into practice, with charity.

Dom Prosper Guéranger's Explanation of the Prayers and Ceremonies of the Holy Mass (hardcover ed. p. 32-33) says:

[While the priest] makes the sign of the Cross upon the Book, and at the place where begins the text of the Gospel…[, the priest and the faithful] at the same time, signs himself on the forehead, the lips, and the breast, asking, in virtue of the Cross, which is the source of all grace, that he may always have the Gospel in his heart, and on his lips, and that he may never be ashamed of it.

^{(I've edited what Dom Guéranger said to apply also to the faithful, not just the deacon. Dom Guéranger is describing a Solemn High Mass, where a priest, deacon who sings the Gospel, and sub-deacon, along with altar servers, assist. The deacon in such Masses does the three signs of the cross to himself just as the faithful do to themselves in all types of Masses, High or Low, before the Gospel. The reason for the three signs of the cross is the same.)}