The atomic numbers of the given lanthanides are:-
$\mathrm{Ce}=58, \mathrm{Eu}=63, \mathrm{Lu}=71$
Since the metallic character decreases from left to right in a period, the order of metallic character for the given metal will be $\mathrm{Lu} < \mathrm{Eu} < \mathrm{Ce}$.
Thus, the basic strength of their hydroxides will be:- $\mathrm{Lu}$ $(\mathrm{OH})_3 < \mathrm{Eu}(\mathrm{OH})_3 < \mathrm{Ce}(\mathrm{OH})_3$.