Student or Learner
what is better to say and why?
Don't let's/let's not.....
Don't let's is not actually incorrect, but it is only seen in older books. Use let's not instead, as bhaisahab posted.
I have seen it in children's books, such as the 'Famous Five' series by Enid Blyton, all written a long time ago...
"Oh, don't let's argue!" pleaded Anne.
It is a general plea to one and all, to abstain from doing something.
'Let's not' is far more common nowadays, but less formal too....
Alas, much of today's speech seems to have lost that subtle touch of elegance.....
I still see a valuable use for "Don't let's.." when one is irritated and being emphatic:
"Don't let's keep going round in circles with this endless discussion. For God's sake, let's make a decision one way or the other. I for one have to get home tonight."
(Born of committee meeting discussions.)