1. Should old acquaintance be forgot,

Question

and old lang syne?

2. Should old acquaintance be forgot,
and should old lang syne be forgot?
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Does #1 mean #2?

auld lang sine or old lang sine means "the old days" according to Cambridge dictionary. [ Auld lang syne means "the old days" in Scots.]

[Auld Lang Syne means ‘for old time’s sake’. - Macmillan Dictionary]

Is 'the old day' the same as ‘for old time’s sake’?

Answer 1

https://www.rd.com/culture/what-does-auld-lang-syne-mean/

Read carefully.