I'm not sure Lolth would want every 3rd son killed. That weakens the race over all and prevents the intense competition that She desires and loves so much. She wants and needs all of the children Her drow can breed since there is such a high death rate.
Yes, she values competittion, deadly serious competittion so that she gets toughest and most cunning souls to her in afterlife whatever plans she haves for them. But she also encourages cruelty and also gambling, killing third son is weakening act for the house and that gambling shows prowess how house fares when it is somewhat diminished slightly. She even herself gambled alot in War of Spider Queen to become greater goddess and she is goddess of chaos so the act itself does not need any logicall explanation or purpose. Also this tests mettle of the mother that is she storng enough name execution newborn baby whatever pains she had endured to bear and birth the child to just sacrafice it to the Lolth.