In article ,
Ed Sirett wrote:

I have assumed that these recesses were to allow air to enter
the cistern during flushing. On some models the lid fits pretty
well and without this opening the flush could be seriously
reduced by the partial vacuum during flushing.

That sounds like a very good reason.

I can't see the back, but looking up from the
bottom of the cistern there also seems to be
some sort of a shallow channel up to the cutout.

--
Tony Williams.