We investigate the impact of center segment dispersity on the phase behavior of 17 lithium salt-doped poly(styrene-block-oligo(ethylene oxide) carbonate-block-styrene) (bSOS) triblock polymers, in which broad dispersity O blocks (D-o = M-w/M-n approximate to 1.45) are situated between narrow dispersity S segments (D-s <= 1.18) with volume fractions f(o) = 0.33-0.69 and total M-n = 11.6-43.8 kg/mol. Broad dispersity bSOS triblocks are synthesized by a tandem polycondensation and atom transfer radical polymerization reaction sequence. Using temperature-dependent small-angle X-ray scattering, we map the morphology diagrams for bSOS samples variously doped with lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) with r = (mol Li+)/(mol ethylene oxide) = 0.00-0.09. As compared to the phase behavior exhibited by 13 LiTFSI-doped, narrow dispersity SOS triblocks with f(o) = 0.30-0.58 and M-n = 7.1-45.2 kg/mol, we demonstrate that O segment dispersity shifts the lamellar morphology window to higher f(o/salt) and the lamellar microdomains dilate at each r value. The critical segregation strength for microphase separation is calculated to be (chi N/2)(ODT) = 10.3-11.1 for r = 0.01-0.05 as compared to the mean-field theory prediction (chi N/2)(ODT) = 8.95. These findings are interpreted in terms of a competition between amplified monomer concentration fluctuations due to O segment dispersity in these high chi/low N triblocks and ordered morphology stabilization due to preferential lithium salt solvation in the O domains.