1. Idea: Two species are isoelectronic if they have the same number of electrons.

2. For an ion:

   • Cation with charge $+n$ has electrons $= Z-n$
   • where $Z$ is the atomic number.

3. Given atomic numbers:

   • $\mathrm{Sm} = 62$
   • $\mathrm{Er} = 68$
   • $\mathrm{Yb} = 70$
   • $\mathrm{Lu} = 71$
   • $\mathrm{Eu} = 63$
   • $\mathrm{Tb} = 65$
   • $\mathrm{Tm} = 69$

Option A: $\mathrm{Sm}^{2+}$ and $\mathrm{Er}^{3+}$

• Electrons in $\mathrm{Sm}^{2+}$: $62-2=60$
• Electrons in $\mathrm{Er}^{3+}$: $68-3=65$

Since $60 \ne 65$, these are not isoelectronic.

✅ A is correct.

Option B: $\mathrm{Yb}^{2+}$ and $\mathrm{Lu}^{3+}$

• Electrons in $\mathrm{Yb}^{2+}$: $70-2=68$
• Electrons in $\mathrm{Lu}^{3+}$: $71-3=68$

Since both have $68$ electrons, these are isoelectronic.

❌ B is not correct.

Option C: $\mathrm{Eu}^{2+}$ and $\mathrm{Tb}^{4+}$

• Electrons in $\mathrm{Eu}^{2+}$: $63-2=61$
• Electrons in $\mathrm{Tb}^{4+}$: $65-4=61$

Since both have $61$ electrons, these are isoelectronic.

❌ C is not correct.

Option D: $\mathrm{Tb}^{2+}$ and $\mathrm{Tm}^{4+}$

• Electrons in $\mathrm{Tb}^{2+}$: $65-2=63$
• Electrons in $\mathrm{Tm}^{4+}$: $69-4=65$

Since $63 \ne 65$, these are not isoelectronic.

✅ D is correct.

Final Answer

The pairs which are not isoelectronic are: $\boxed{A, D}$

This matches the stored correct answer.