Most peat based commercial potting mixes are pH balanced, otherwise they would be excessively acidic due to the peat (pH of 3.5-4.0). They should test out at around 6.0-6.5, which is the preferred range for most plants. So no, I doubt you need to add lime unless you are adding other, highly acidic ingredients.

1 part / 15% of the mix won't buffer the rest of the bark, in my opinion, so I would still add the Lime (or perhaps just slightly less Lime). I, too, use a commercial potting mix in lieu of the peat, and I add the Lime.

Josh

Thank you both!