According to my understanding Lagrange points L1, L4 and L5 can form because gravitation pull can cancel out here as these are between Sun and Earth (where gravitational pull is in two different directions).
This is a misconception. The net gravitational attraction is directed toward the Sun at the Sun-Earth L1 point. The point at which gravitational acceleration is canceled is closer to the Earth and is uninteresting.
It is the net gravitational attraction plus the centrifugal acceleration about the Sun-Earth barycenter that cancels, and then only when this is done the perspective of a frame that rotates at one revolution per sidereal year. (There is no centrifugal acceleration in an inertial frame.)
The existence of the linear Lagrange points is perhaps easier to understand from the perspective of an inertial frame whose origin is the center of mass of the two massive bodies (e.g., the Sun and the Earth). The only forces one needs to consider from such a perspective are gravitational acceleration of the third body (which has negligible mass) toward the two massive bodies.
The L1 point is where the net gravitational acceleration is just enough to make the third body orbit the center of mass at the same rate as the rate as the two massive bodies orbit one another. Keep in mind that the two massive bodies orbit one another at $\omega^2 = \frac{G(M_1+M_2)}{r^3}$. The net gravitational acceleration points toward to the less massive body at distances close to the less massive body, so obviously not good. There's a point between the two bodies where the net gravitational acceleration is zero. That once again is not good. With increasing distance from the less massive body (decreasing distance from the more massive body), acceleration toward the more massive body dominate. There's a point, the L1 point, at which the net acceleration is exactly enough to make an object of negligible mass orbit the center of mass at the same rate as the two massive bodies orbit one another.
The L2 point is perhaps even easier to understand from the perspective of an inertial frame. Beyond the less massive body, the acceleration vectors toward the two massive bodies both point toward the center of mass. At distances very close to the less massive body the net acceleration is too great. At extreme distances, the net acceleration is near zero. There's an intermediate point, the L2 point, where the net acceleration is exactly right.
A similar line of thinking applies to the L3 point: The acceleration vectors toward the two massive bodies both point toward the center of mass. There is a non-intuitive aspect regarding the L3 point, which is that the distance between the center of mass and the L3 point is greater than the distance between the center of mass and the less massive body, but is less than the distance between the two massive bodies.
Aside: To understand the instability of the linear Lagrange points it is much easier to look at things from the perspective of a rotating frame.
