If we don't leave till after lunch we'll be cutting it very fine.
I understand it to mean: "If we don't leave after lunch, we'll be cutting it very fine." (In the event of our not leaving immediately after lunch, we will leave ourselves just enough time to do something.)
But why is till in that position?
The word till means until
Until means
[often preceded by up] in or throughout the period before
In the context of your sentences, the first means
if we [don't leave in any of the periods before, but] leave [immediately] after lunch, we'll be cutting it fine.
The second sentence means
If we don't leave [immediately] after lunch, we'll be cutting it very fine.
The first sentence contemplates leaving at a variety of times up to the period immediately following lunch. The second sentence only contemplates one departure time - immediately following lunch.
Till is the older version of until , as described in another question here:
What is the difference between "till" and "until"?
Till is indeed older and the two can be used pretty much interchangeably.
As a suggestion, you could also rewrite the sentence like so:
If we don't leave 'til after lunch, we'll be cutting it very fine.
'til is an abbreviation of 'until'.
In contrast to what @fuzzyanalysis said, my understating of the sentence containing till is:
If we do not leave before lunch is finished, we'll be cutting it very fine.
The subtle difference is that there is no need in interpreting immediately.
Also the sentence
If we don't leave after lunch, we'll be cutting it very fine.
says nothing about immediately after lunch or one hour after lunch or whatever, just after lunch.
