Statement-I: La(OH)₃ to Lu(OH)₃ basic strength decreases
Statement-II: La(OH)₃ to Lu(OH)₃ ionic character decreases

Basicity of hydroxides of lanthanides decreases from La to Lu.

Reason: Due to Lanthanide contraction the Ln⁺³ ion sizes from La to Lu decreases, hence $\mathrm{Ln}-\mathrm{OH}$bond length decreases, bond strength increases, ionisation of  $\mathrm{Ln}-\mathrm{OH}$ bond  decreases(ionic character decreases) from $\mathrm{La}{\left(\mathrm{OH}\right)}_3 \mathrm{to} \mathrm{Lu}{\left(\mathrm{OH}\right)}_3$