The present study aims at introducing a new concept of layer of LB-valued general fuzzy automata (LB-valued GFA) where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a lattice-ordered monoid. In general, it demonstrates that the layer plays a key role in the algebraic study of LB-valued GFA by characterizing the concepts of subautomata and separated subautomata of an LB-valued GFA in terms of its layers. In other words, it highlights that every LB-valued general fuzzy automaton has at least one strongly connected subautomaton. In specific, the characterization of some algebraic concepts such as subautomaton, retrievability and connectivity of an LB-valued GFA in terms of its layers is provided. In addition, it is shown that the maximal layer of a cyclic LB-valued general fuzzy automaton and minimal layer of a directable LB-valued general fuzzy automaton are unique. Finally, we investigate the different poset structures associated with an LB-valued general fuzzy automaton, demonstrating some of these posets as finite upper semilattice, and introducing the isotone Galois connections between some of the pairs of the posets/finite upper semilattices introduced.