However, Sars on Friday would not confirm his resignation.
“We don’t comment on the movement of staff,” spokeswoman Marika Muller said.
Lackay would also not comment on the matter saying he was not permitted to speak to the media.
The troubled revenue service has seen a number of senior officials resign or be suspended recently, some ending up in the Labour Court.
This has been amid allegations of a special projects unit engaging in illegal activities in Sars.