The action of local anaesthetics depends on the concentration gradient, the speed of absorption and the affinity of the drug for neuronal tissue.
It is also the amount of free base that is present that is important because this is the lipid soluble component.
In acidic environments, e.g. infection, the amount of free base is usually reduced, in accordance with the Henderson-Hasselbalch equation. This means less LA can penetrate to the inside of the cell.
Since the receptors for the sodium ion channels, which effect the local anaesthetic action, are on the inside of the cell this renders the anaesthetic less effective.