Basically tidying up.
Names are as vital to a "predicate language" as predicates; the things with holes are
useless without something to fill the holes, and those can't be all bound variables, else we never get down to reference. So, names are essential, and, for a good formulation, they need to be immediately distinct from predicates (and variables, the other usually considered essential). So, Lojban is in fine shape as of now, except for the peculiarity of introducing every name, in its referential use, with {la}, which looks like a gadri (indeed, is one in the grammar). But names, properly speaking (end in a consonant, maybe surrounded by pauses) don't need a gadri, they are terms by their nature, just like the pronouns and variable. One can imagine JCB, noticing that names apply to sets and masses (what he had in the way of pluralities) as well as individuals, and having devised forms for these, decide that he needed a form for the individuals to complete the pattern matching {le} and {lo}and so added the superfluous {la}. (I
don't bleieve this story at all. Although I long ago surrendered my ancient -- including pre-1960 -- Loglan material and so don't know the history of {la}, my belief is that JCB was a crypto Mergist from the beginning, taking names to be predicates of the peculiar autonymous sort and requiring {la} to bring them into referential use.) Well, not quite superfluous, since it does allow predicates to be used as names in just the way the Mergist would have them. Presumably {doi} and the like work as well to distinguish what follows as a nonce name.
Loglan {me} is not quite the same as Lojban (assuming that is now pinned down a bit). Its original use was to attach names into compounds: a 'me la Djenis' procedure for deriving new predicates (pre GMR) and, of course, the 'me la me' hole in the grammar. It expanded somewhat to allow other arguments than names, but always kept the sense of proprietary interest, pertaining to in a
special way. In short, it was used to incorporate names and then descriptions into "metaphors" (i.e. tanru) as full members on a par with predicates. But it never came to be a general "related to", nor did it develop a second place, and it certainly never meant "is a member of/ avatar from/ chunk of" (not that these latter are really in Lojban, but they do turn up from time to time).