During bromination of phenol, Lewis acid is not necessary required because of:

\(+R\) effect of \(-OH\) group

The correct answer is option 3. \(+R\) effect of \(-OH\) group.

During the bromination of phenol, a Lewis acid catalyst (such as \(FeBr_3\)) is often used to facilitate the reaction by complexing with the bromine molecule and enhancing its electrophilicity. However, in the absence of a Lewis acid catalyst, the reaction can still proceed due to the presence of certain electronic effects. Let us analyze each option:

1. Electromeric effect: The electromeric effect involves the shifting of π-electrons in a molecule due to the influence of an adjacent atom or group. While this effect can influence the reactivity of a molecule, it is not directly relevant to the necessity of a Lewis acid catalyst in the bromination of phenol.

2. Inductive effect of \(-OH\) group: The inductive effect refers to the polarizing effect of a functional group due to differences in electronegativity. The \(-OH\) group in phenol exhibits a slight electron-withdrawing (inductive) effect. However, this effect alone is not sufficient to explain the bromination of phenol without a Lewis acid catalyst.

3. +R effect of -OH group: The +R effect (also known as resonance effect) involves the donation of electrons through resonance into a conjugated system. The -OH group in phenol exhibits a resonance effect, which can stabilize the intermediate formed during the bromination reaction. However, this effect is not directly related to the necessity of a Lewis acid catalyst.

4. Deactivating effect of -OH group: The -OH group in phenol is known to be ortho-para directing in electrophilic aromatic substitution reactions, due to its electron-donating resonance effects. However, this effect does not explain the lack of necessity for a Lewis acid catalyst in the bromination of phenol.

Given these explanations, the most relevant option is: 3. \(+R\) effect of \(-OH\) group.

The resonance effect (+R effect) of the -OH group in phenol can stabilize the intermediate formed during the bromination reaction, making it less reliant on a Lewis acid catalyst for reaction initiation. This resonance stabilization helps facilitate the reaction, allowing bromination to occur without the necessity of a Lewis acid catalyst.