The 'lost penny' in Zen Cart refers to the one unit difference between invoice total and addition of intermediate numbers (cart total + shipping +...).
It is due to rounding errors and is not a problem specific to ZC, it is in any accounting.

When calculating total, Zen Cart uses 'high precision' calculation (no rounding before display, in ZC v2.0.0), but on invoice you have to round item prices, cart subtotal, shipping cost, discounts and tax... And they have to equal total when added, which sometimes does not work because of differences in calculation methods and more importantly in rounding time.
This problem has a high probability of being visible when there are lots of multiplications involved: High quantity of items in cart, tax calculation and the worst, currency conversions with a high rate (> 100).

There was some attempt to fix this in ZC by rounding numbers at the right place, but it was a bad idea. This method would work in certain cases but add more error in others. What was done in recent version of ZC (v2.0.0 in preparation) was to remove these rounding. Results are more consistent but still sometimes, depending on numbers, the lost penny appears (or disappears) on the invoice.
There is a case where this small error is amplified, when converting, for example, from USD to JPY at a rate of 155. Lost of few tenths of a penny when converted become few dozens. Hopefully, ZC uses at least four decimals, which is good as long as no rounding is done. Although, when multiplying by 155, one or two more decimal might be better.

The lost penny is mathematically inevitable, but it can be moved... By detecting when it appears, you can correct it. Then all numbers on the invoice will add correctly. The only drawback is that if you compare the same invoice content, but one printed with prices without tax and the other with tax included, there will be one penny difference in final total. But as we generally use only one type of invoice at a time, it will make the lost penny disappear!

I modified ot_total.php to do that. You can take a look at it on GitHub here.