There are usually two reasons for using a lining on a WPB fabric:
i) to protect the coating from abrasion (if it's a 2-layer fabric);
ii) to stop you noticing condensation.
For a bivvy, I can't really see that either is applicable; you don't get the same degree of continuous movement that you do with clothing (so wear shouldn't be a big issue), and any condensation (of sweat) is likely to get to your sleeping bag through a liner, anyway... Since you're not very active when in a bivvy, condensation is likely to be less of an issue than in clothing (assuming you're venting your breath somehow).