Identify the type of compound

$Cs$ is an alkali metal, so it almost always forms the ion $Cs^+$.

Therefore, option A is immediately suspicious because $Cs^{3+}$ is not a stable/common oxidation state for cesium.

Interpret the formula $CsI_3$

Since cesium forms $Cs^+$, the remaining part must carry a charge of $-1$:

$CsI_3 = Cs^+ + (I_3)^-$

So the species present is the polyhalide ion $I_3^-$, called the triiodide ion.

Nature of polyhalide salts

Compounds like $KI_3$, $CsI_3$ etc. are known as polyhalide salts. They are ionic solids containing:

$M^+ + I_3^-$

where $M^+$ is an alkali metal cation.

Check each option

A: "it contains $Cs^{3+}$ and $I^-$ ions"
This is incorrect because cesium does not form stable $Cs^{3+}$ in such compounds.

B: "it contains $Cs^+$, $I^-$ and lattice $I_2$ molecule"
Although $I_3^-$ can be conceptually viewed as $I^- + I_2$, the actual ionic species in the crystal is represented as $I_3^-$. Hence this is not the best/correct description for the compound.

C: "it is a covalent molecule"
Incorrect. $CsI_3$ is an ionic polyhalide salt.

D: "it contains $Cs^+$ and $I_3^-$ ions"
This is correct.

Final answer

The correct statement is:

$\boxed{\text{D: it contains } Cs^+ \text{ and } I_3^- \text{ ions}}$