a multi dimensional lattice is a spatial structure, computation can be distributed over space in the lattice. (I'm a fan, following the project)

BitLattice is a post-blockchain system, so its not a chain. The chain structure is limited, blockchains for example have to let a single node add hundreds of transactions at a time, into a block, to prevent collisions that would occur if all nodes appended transactions simultaneously, and so proof-of-work or proof-of-stake is used to introduce a bottleneck. In BitLattice, because the lattice has not just one position for new transactions (the next element in a chain) but thousands or millions in a vast multidimensional lattice, how I've understood it is that nodes can work in parallel, and then synchronise with one another while adding new transactions in parallel, all at once, through a toroidal network where replication of transactions is very very fast.

So since BitLattice is not a chain, the probability of collisions when appending transactions are very small (whereas in a chain the probability is near 100%) and so almost insignificant.

(this is my interpretation of why BitLattice is not a chain, and what the benefits of that are, it may not be accurate)

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.

could the toroid based network protocol be a good infrastructure for replicating information on a network in general, like for example, as an alternative or a competitor to TCP/IP, BitTorrent, or IPFS?

is the toroid based network protocol for replicating transactions between nodes, rather than the topography of the chain (a hyper-lattice) ?