Phenolic group can be identified by a positive

The correct option is Phthalein test.

Phenols containing a free para-position undergo a condensation reaction when heated with phthalic anhydride in the presence of concentrated sulfuric acid:
$H_2{\mathrm{SO}}_4$
to form a dye called phenolphthalein.

When this reaction mixture is treated with a dilute sodium hydroxide solution:
$\mathrm{NaOH}$
the phenolphthalein formed turns into its sodium salt, which displays a characteristic deep pink or red-violet color. This color change confirms the presence of a phenolic group.

Let us look at why the other options are incorrect:

Lucas test is used to distinguish between primary, secondary, and tertiary alcohols using a mixture of concentrated hydrochloric acid and anhydrous zinc chloride:
$\mathrm{HCl}/{\mathrm{ZnCl}}_2$
Alcohols react at different rates to form insoluble alkyl chlorides, resulting in turbidity.

Carbylamine test is used to detect primary aliphatic and aromatic amines, which produce a foul-smelling substance called isocyanide (carbylamine).

Tollen's test is used to identify aldehydes, which reduce Tollen's reagent to produce a shiny silver mirror.