The IUPAC name for the complex compound Li[AlH4] is: (A) Lithium aluminium hydride (B) Hydride aluminium lithium (III) (C) Lithium tetrahydridoaluminate (III) (D) Lithium tetrahydridoaluminate (I)

To determine the IUPAC name for the complex compound \( \text{Li}[ \text{AlH}_4 ] \), let’s analyze its structure and components:

1. **Identify the components**:
- The compound consists of lithium (\( \text{Li} \)) and the anion \( [\text{AlH}_4]^{-} \).
- \( \text{AlH}_4 \) represents an aluminium atom bonded to four hydride ions (\( \text{H}^{-} \)).

2. **Understanding the structure**:
- The aluminium in this complex has a formal oxidation state of -1 (since it is coordinated to four hydride ions).
- Lithium, being an alkali metal, carries a +1 charge.

3. **Naming conventions**:
- In IUPAC naming, the cation (in this case, lithium) is named first, followed by the name of the anion.
- The anion \( [\text{AlH}_4] \) is referred to as "tetrahydridoaluminate" since it consists of aluminium and four hydride ions.

4. **Combining the names**:
- The overall name starts with "lithium" (for the cation) and then "tetrahydridoaluminate" (for the anion).
- Since aluminium has an oxidation state of +1 when combined with the lithium cation, we represent it as \( \text{aluminate (I)} \) in the name.

5. **IUPAC name selection**:
- The correct IUPAC name combines both parts:
- "Lithium" for the lithium ion.
- "tetrahydridoaluminate" for the aluminium complex with hydride ligands.
- Therefore, the complete name is **Lithium tetrahydridoaluminate (I)**.

### Conclusion

The correct answer is:
**(D) Lithium tetrahydridoaluminate (I)**.