I am still learning about BitLattice. From how I understand it so far, BitLattice has refined some of the ideas behind Tangle and Byteball, and done so to the point that it is almost not comparable. Just like in Tangle and Byteball, transactions are appended to previous transactions, but besides that, BitLattice also organises transactions into a fixed topology (the hyper-lattice) which in itself makes it possible to build functions on top of it. The lattice is a spatial field, which means that certain types of mathematics that apply to spatial fields can be performed on top of the lattice. The possibility for lattice-based mathematics, including lattice-based cryptography, and also wave functions throughout the lattice as a spatial field for proof-of-structure, and similar things, are what is made possible with a lattice, and so yes, BitLattice appends transactions in ways that are slightly similar to Tangle and ByteBall, but it does so in ways that make all sorts of new math possible.