Now consider this:
"In the book, at page 333, the reporters revealed their story "quoted anonymously Deep Throat's remark that there were gaps of 'a suspicious nature' which 'could lead someone to conclude that the tapes have been tampered with.'" In the Nov. 8, 1973 issue of the Post, the same quote as in the book was attributed to one of their White House sources."
The tapes were turned over to investigators in early November, shortly after Archibald Cox was fired.
There's no reason to assume that White House lawyers knew what was on the tapes or that they knew anything about the erasures until after they were analyzed by investigators. I would think that FBI insiders would be among the first to know of irregularities, most likely before White House officials or Sirica.
(Except, perhaps, Rose Mary Woods. ;-)