First of all, this link has a beautiful explanation on what Lagrange points are.
L4 and L5 exist because the combined pull of the two bodies system (e.g. Earth - Sun, Jupiter - Sun) makes whatever is placed there orbit around the centre of mass of the two bodies system, rather than the bigger object itself. So basically everything placed in L4 and L5 follows the same orbit as the smaller body.
The difference with L1/L2/L3 is that L4 and L5 are stable equilibrium points(for the mass ration $M_1/M_2 \geq 25$), while L1-L3 are unstable. Stable means that, if you place an object there and then move it a little bit, it will go back to where you placed it. Unstable means the opposite.
So it is true that the Jupiter gravity perturbs anything you put in the Lagrange point of Earth, but since it is stable equilibrium it will not be enough to get it out.