1. Check each statement one by one.

2. Option A: d-Block elements show irregular and erratic chemical properties among themselves

This is true.

Reason:

• In the $d$-block, electrons are added to the penultimate $d$-subshell.
• Because of small differences in energies of $ns$ and $(n-1)d$ orbitals, these elements show:
  • variable oxidation states,
  • irregular trends in atomic size,
  • magnetic behavior,
  • catalytic properties.

So, chemical properties are indeed somewhat irregular and erratic across the series.

3. Option B: La and Lu have partially filled d orbitals and no other partially filled orbitals

This is true.

Electronic configurations:

• $\mathrm{La} = [Xe]5d^1 6s^2$
• $\mathrm{Lu} = [Xe]4f^{14}5d^1 6s^2$

In both cases:

• the $d$ orbital is partially filled ($d^1$),
• there is no other partially filled subshell.

Hence this statement is correct.

4. Option C: The chemistry of various lanthanoids is very similar

This is true.

Reason:

• Lanthanoids mainly show the oxidation state $+3$.
• The differentiating electrons enter the inner $4f$ orbitals.
• Since $4f$ electrons do not participate much in bonding, their chemical properties remain very similar.

So this statement is also correct.

5. Option D: 4f and 5f orbitals are equally shielded

This is incorrect.

Reason:

• $4f$ orbitals are poorly shielded.
• $5f$ orbitals are also shielded poorly, but they are less deeply buried and participate more in bonding than $4f$ orbitals.
• Hence, $4f$ and $5f$ orbitals are not equally shielded.

This difference is one reason actinoids show more variable oxidation states compared to lanthanoids.

6. Conclusion

The incorrect statement is: $\boxed{D}$