An estimated 15-20% of patients who are treated for pulmonary tuberculosis (TB) are culture-negative at the time of diagnosis. Recent work has focused on the existence of differentially detectable Mycobacterium tuberculosis (Mtb) bacilli that do not grow under routine solid culture conditions without the addition of supplementary stimuli. We identified a cohort of TB patients in Lima, Peru, in whom acid-fast bacilli could be detected by sputum smear microscopy, but from whom Mtb could not be grown in standard solid culture media. When we attempted to re-grow Mtb from the frozen sputum samples of these patients, we found that 10 out of 15 could be grown in a glycerol-poor/lipid-rich medium. These fell into the following two groups: a subset that could be regrown in glycerol after "lipid-resuscitation", and a group that displayed a heritable glycerol-sensitive phenotype that were unable to grow in the presence of this carbon source. Notably, all of the glycerol-sensitive strains were found to be multidrug resistant. Although whole-genome sequencing of the lipid-resuscitated strains identified 20 unique mutations compared to closely related strains, no single genetic lesion could be associated with this phenotype. In summary, we found that lipid-based media effectively fostered the growth of Mtb from a series of sputum smear-positive samples that were not culturable in glycerol-based Lowenstein-Jensen or 7H9 media, which is consistent with Mtb's known preference for non-glycolytic sources during infection. Analysis of the recovered strains demonstrated that both genetic and non-genetic mechanisms contribute to the observed differential capturability, and suggested that this phenotype may be associated with drug resistance.