# Class of the language only containing the empty string?

$L = \left \{ \epsilon \right \}$
Clearly this language is finite so this must be a regular language.
Now since every regular language is Context Sensitive, $L$ is a CSL.
We can define the grammar for $L$ as :
$S\rightarrow \epsilon$
Now since $L$ is a CSL, this grammar must be a Context Sensitive Grammar. But from the definition of a Context Sensitive Grammar:

A Context sensitive grammar is any grammar in which the left side of each production is not longer than the right side.

But here
$\left | S \right | > \left | \epsilon \right |$
This issue is covered in wikipedia's article on noncontracting grammars. Such grammars do not allow deriving the empty string, which is no problem when one considers languages $L\subseteq A^+$. When one wants to allow the empty string, a special case is made and the rule $S\to\lambda$ is allowed with ugly side conditions ($S$ cannot appear in a right-hand side).
BTW your reasoning has a flaw. You say that the language is CSL (correct) and $S\to\lambda$ is a grammar for it (correct), thus that grammar is CS. That implication is incorrect. You can only deduce that there exists a CS grammar for it. But you are right in thinking that any such grammar must have a contracting rule.