Due to lanthanide contraction, the size of $M^{3+}$ ions $\left[i e, Lu ^{3+}, Eu ^{3+}, Yb ^{3+}\right.$ and $\left. Ce ^{3+}\right]$ decreases and thus, the basic strength of their hydroxides decreases.
The order of size of given $M^{3+}$ ions is
$Ce ^{3+}> Eu ^{3+}> Yb ^{3+}> Lu ^{3+}$
$\therefore $ The order of basic strength of hydroxides is
$\underset{\text{(most basic)}}
{{Ce ( OH )_{3}}}>\, Eu ( OH )_{3}>\, Yb ( OH )_{3}>\, Lu ( OH )_{3}$