Final answer:
The condition necessary for a sp³-hybridized atom to display asymmetry is a lack of lone pairs.
Step-by-step explanation:
The condition necessary for a sp³-hybridized atom to display asymmetry is a lack of lone pairs. When an atom is sp³-hybridized, it forms four equal hybrid orbitals that are arranged in a tetrahedral geometry. These hybrid orbitals are involved in bonding and do not contain any lone pairs. As a result, the molecule will have a symmetric shape. It is only when the atom lacks lone pairs that the molecule can have a non-symmetric, or asymmetric, shape.