Do Slater's rules apply to neutral lithium (at least approximately)? For lithium, the electronic configuration is $\ce{(1s)^2(2s)^1}$. I tried to calculate $Z_{eff}$ for the $\ce{2s}$ orbital of the neutral atom as follows:

$$Z_{eff} = Z-\sigma$$
$$Z_{eff} = 3-(2\times0.3)$$
$$Z_{eff} = 2.4$$

But the Wikipedia article's table of effective nuclear charges (linked below) states that $Z_{eff}$ is 1.279 for the $\ce{2s}$ lithium orbital, which is not even close to my answer (above). So do Slater's rules not apply to lithium or I have done something wrong?

Wikipedia article: https://en.wikipedia.org/wiki/Effective_nuclear_charge
You need to use the factor of 0.85 for each of the $\ce{1s}$ electrons:
$$Z_{eff} = 3 - (2\times 0.85) = 1.3$$
as per rule #2 in the Wikipedia article:


  
  If the group is of the [s p] type, an amount of 0.85 from each electron with principal quantum number n one less than that of the group, and an amount of 1.00 for each electron with principal quantum number two or more less.
  


The $\ce{1s}$ electrons both qualify as having "a principal quantum number $n$ one less than that of the group" (here, the principal quantum number of the group of the $\ce{2s}$ electron is 2). Here is a nicely worked example for further edification.