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The model divides time between now and the option's expiration into N discrete periods. At the specific time n, the model has a finite number of outcomes at time n + 1 such that every possible change in the state of the world between n and n + 1 is captured in a branch. This process is iterated until every possible path between n = 0 and n = N is mapped. Probabilities are then estimated for every n to n + 1 path. The outcomes and probabilities flow backwards through the tree until a fair value of the option today is calculated.
The simplest lattice model for options is the binomial options pricing model, while a more sophisticated variant is the Trinomial tree. For multiple underlyers multinomial lattices  can be built, although the number of nodes increases exponentially with the number of underlyings. For Interest rate derivatives the lattice is built by discretizing a short rate model, such as Hull-White or Black Derman Toy, or a forward rate-based model such as the LIBOR market model or HJM.
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