Why should I add lithium bromide to my GPC eluent?
The answer to my question appears to be in a 1977 paper by Nancy D Hann (DOI: 10.1002/pol.1977.170150604; full citation below). In it, she compares GPC of polyurethane in DMF with and without added LiBr. The chromatograms with no added LiBr show multiple peaks. The chromatagrams with added LiBr show just a single peak. The addition of LiBr also shifts the peak to later elution volume. 

Hann explains these results by the polymer having a strong polar interaction with the pure solvent. This causes a higher effective hydrodynamic radius, resulting in the earlier elution time. The polar interactions also case aggregation of the polymer, giving multiple peaks. Adding a salt breaks up the polar interactions, giving just a single, later, peak.



Hann, N. D. (1977). "Effects of lithium bromide on the gel-permeation chromatography of polyester-based polyurethanes in dimethylformamide." Journal of Polymer Science: Polymer Chemistry Edition 15(6): 1331-1339.