fitLogNormal is based on the MetaStats package maintained by the MetagenomeSeq developers. It is not clear what this permutation T-Test provides that is not provided by fitFeatureModel with a equivalent number of iterations. 

Is this simply the test that fitFeatureModel calls to do its job?

MetagenomeSeq has a number of tests implemented and available for users, including Fisher's exact test for presence / absence of a feature (fitPA) and a measure of the discovery odds (based on # reads) (fitDO).

fitFeatureModel does not call fitLogNormal. fitLogNormal is solely a permutation based t-test on the log-transformed data - this is an expansion to the main test provided by metastats (multiple covariates could not be included in metastats).