This effect activates mandatorily when "Ally of Justice Omni-Weapon" destroys a LIGHT monster by battle and sends it to the Graveyard (= at the end of the Damage Step).[1]
If the effect of "Ally of Justice Omni-Weapon" is activated, the part of the effect that draws 1 card is always applied, but you can choose not to apply the part of the effect that Special Summons the drawn card.[1]
Since Special Summoning the drawn card is part of the same effect, it does not start a new Chain Link.[1]
This effect cannot be activated if "Ally of Justice Omni-Weapon" battles a LIGHT monster with the same ATK and both monsters are destroyed.[1]