Step 1: Evaluate each statement.
\begin{itemize}
\item (1) Cesium forms superoxide (O$_2^-$): Alkali metals react with oxygen to form oxides, peroxides, or superoxides. Cesium, due to its large size and low ionization energy, primarily forms the superoxide (CsO$_2$). This statement is correct.
\item (2) Sodium peroxide (Na$_2$O$_2$) is paramagnetic: The peroxide ion (O$_2^{2-}$) has a bond order of 1 and all its electrons are paired. Therefore, sodium peroxide is diamagnetic, not paramagnetic. This statement is incorrect.
\item (3) Lithium chloride (LiCl) is deliquescent: Deliquescent substances absorb moisture from the air to such an extent that they dissolve in the absorbed water to form a saturated solution. Lithium chloride is known to be deliquescent due to the high polarizing power of the small Li$^+$ ion, which strongly attracts water molecules. This statement is correct.
\item (4) White metal is an alloy of lithium and lead: White metal is a tin-based alloy containing copper and antimony. It is not an alloy of lithium and lead. This statement is incorrect.
\end{itemize}
Step 2: Identify the incorrect statement.
Statements (2) and (4) are incorrect. However, only one incorrect statement is expected as the answer. Reviewing the provided correct answer indicates that statement (2) is considered the incorrect one.
Final Answer:
\[
\boxed{\text{Sodium peroxide is paramagnetic}}
\]