Use the known general properties of lanthanoids in the +3 oxidation state

Lanthanoids predominantly form $\mathrm{Ln^{3+}}$ ions. Their chemistry shows some standard trends:

• compounds are largely ionic,
• ionic radii decrease across the series due to lanthanoid contraction,
• hydroxides are generally basic,
• many $\mathrm{Ln^{3+}}$ ions are coloured because of partially filled $4f$ orbitals.

Check each option

Option A: "Because of the large size of the $\mathrm{Ln^{3+}}$ ions the bonding in its compounds is predominantly ionic in character."

This is correct. Lanthanoid ions are large electropositive metal ions, so their compounds are mainly ionic.

Option B: "The ionic sizes of $\mathrm{Ln^{3+}}$ decrease in general with increasing atomic number."

This is correct due to lanthanoid contraction.

Option C: "$\mathrm{Ln^{3+}}$ compounds are generally colourless"

This is incorrect. Many $\mathrm{Ln^{3+}}$ ions are coloured because of $f$-$f$ electronic transitions. Although some ions like $\mathrm{La^{3+}}$ and $\mathrm{Lu^{3+}}$ are colourless, the general statement "generally colourless" is false.

Option D: "$\mathrm{Ln^{3+}}$ hydroxides are mainly basic in character."

This is correct. Lanthanoid hydroxides such as $\mathrm{Ln(OH)_3}$ are basic; in fact, their basicity decreases somewhat from La to Lu, but they remain mainly basic.

Conclusion

The incorrect statement is:

$\boxed{\text{C}}$

Comparison with stored correct answer

Stored correct answer = C

My derived answer = C

Hence, they agree.