Model, actress and radio personality Pearl Thusi was in a car accident that left her and her daughte.
Luyt, speaking on Ballz Radio, questioned the GLRU's solvency, management and business acumen, accusing Lions management since he left office in 2000 of squandering a vast fortune he left behind.
Luyt said that there was "R85-million in cash reserves and no debt" when he retired 12 years ago and that it was now gone.
De Klerk said: "Some of Dr Luyt's comments are mischievous and I wasn't around when he supposedly left this great amount of money behind at the GLRU.
"I can give you an assurance that all monies are accounted for and there was no wrongdoing.
"Perhaps Dr Luyt's health at 80 years of age is not that great. I would urge him to enjoy his retirement and if he wants to advise the GLRU he is welcome to give me a call instead of sensationalising our situation."
De Klerk did concede that things weren't great at the Lions: "The union is facing challenges and has faced some challenges in the past few years but we will come through that.
"(Luyt) has had his time at the top and now he must let us get on with it. I'm often asked how I would shape in modern rugby (De Klerk played for the Springboks between 1974-81) and I reply that I wouldn't last more than 10 minutes.
"But the guys would have to get through those 10 minutes because we would play old rules. The moral is that with respect to Dr Luyt, these are different times and running a union is vastly different from what it was like in his day.
"The budgets are bigger and allocated differently. He made a reference that criticised the union for contracting junior players, but that's an absolute reality of the modern game. You have to contract good juniors at great expense," he said.
De Klerk also confirmed that the GLRU is taking further legal advice after losing an arbitration hearing with junior Super Rugby franchise partners the Leopards and Mpumalanga Pumas last week. The GLRU was ordered to pay the Leopards R2.565-million in franchise fees and there is a possibility that another R6.6-million might have to be paid to both junior partners as well.