I got the following setting:
Consider the decomposition $L=H+\sum_{\alpha\in \phi}L_{\alpha}$,
where the sum is a direct sum, the $L_{\alpha}$ are the root spaces and $H$ is nilpotent (because its abelian).
This is from the last step of the proof of Serre's theorem (c.f. James E. Humphreys Thm. 18.3).
The question is now: Why $H$ is self-normalizing?
In Humphreys book it is proved long before Theorem 18.3, that every Cartan subalgebra $H$ is self-normalizing. Also, there is the following exercise in Humphreys book (and since you say that $H$ is abelian, I suppose that this is what you want):
Exercise 5: If L is semisimple, H a maximal toral subalgebra, prove that H is self-normalizing.
The solution is online here.