The IUPAC name for the complex compound Li[AlH₄] is

lithium tetrahydridoaluminate (III)

The correct answer is option (3) lithium tetrahydridoaluminate (III).

The IUPAC name for a coordination complex is based on the following rules:

The ligand name is given first, followed by the name of the metal ion.

If the ligand is a polydentate ligand, the prefix "bis", "tris", etc. is used to indicate the number of donor atoms in the ligand.

The oxidation state of the metal ion is given in parentheses after the metal name.

In the case of the complex Li[AlH₄], the ligand is tetrahydroaluminate, which is a polydentate ligand with 4 donor atoms. The oxidation state of aluminum in the complex is +3. So, the IUPAC name of the complex is lithium tetrahydridoaluminate (III).

The other options are incorrect. Option (1), lithium aluminium hydride, is incorrect because it does not specify the oxidation state of aluminum. Option (2), hydrido aluminium lithium (III), is incorrect because it does not use the correct ligand name. Option (4), lithium tetrahydridoaluminate (I), is incorrect because the oxidation state of aluminum is +3, not +1.