There's many ways to calculate a $C_6$ value, for which it doesn't matter whether the element is heavier or lighter than Xe.
One of the simplest equations for $C_6$ is in the abstract of a 1931 paper by Slater and Kirkwood (often called the Slater-Kirkwood approximation):

Therefore we have (in the notation of Brandt in 1955, and probably others between 1931-1955):
$$\tag{1}
C_6 = -\frac{3}{4}\left(a_0N\alpha^3\right)^{1/2}e^2,
$$
with $a_0$ being the Bohr radius, $N$ being the number of electrons in the molecular valence shell, $\alpha$ being the average dipole polarizability, and $e$ being the charge of an electron.
For a heteronuclear system another simple formula is given here:
$$\tag{2}
C_6^{AB} = -\frac{3}{2}\frac{I_AI_B}{I_A+I_B}\alpha_A\alpha_B,
$$
with $I_A$ and $I_B$ being the first ionization energies for the systems $A$ and $B$, and $\alpha_A$ and $\alpha_B$ being again their average dipole polarizabilities.
You are correct that other formulas exist, for example, I found at least two in this paper:


I tried to turn the question What are the different ways of calculating dispersion constants? into a list of all the known methods to approximate $C_6$, but I wanted it to be in the form of one-topic-per-answer with each user explaining just one method (otherwise you might get 10 answers from me, which I think would look weird).
Beyond the element Xe, relativistic effects will become quite important when attempting to calculate the dipole polarizability $\alpha$ or the ionization energy $I$ using ab initio methods. Another famous relativistic effect was described in this 1948 paper by Casimir and Polder, in which they showed that for very large distances the $C_6$ actually becomes a $C_7$.