"We'll do it in a..."

Solution 1:

Wiktionary has the following entry:

in a one-er (not comparable)
(informal) in one attempt
You can probably empty your glass in a one-er, there's not much left.

In a oner is given as an alternative form, and Oxford Dictionaries Online has oner. I would tend to go with oner, since (1) it looks more authentic, (2) it's in the Oxford Dictionary, and (3) one-er reminds me of an uninformed person's attempt at translating it from spoken to written English.

It appears to be a British term, which is probably why I wasn't familiar with it.

The only way I can possibly make a stab at guessing which is more popular is by Google, so the rest of this answer isn't worth all that much... "in a oner" has 448 results and "in a one-er" has 356.

Solution 2:

From OED:

oner - 2 colloq. Something consisting of, denoted by, or in some way characterized by the number one. spec. one pound; one hundred pounds.

I suppose in your context, the lecturer either meant a one-liner (he'd write a one-line expression implementing the final few steps/calculations on the blackboard), or that he'd go through the final steps in a single uninterrupted section of his presentation, without pausing to allow questions, etc.