  We investigate the lazy burning process for Latin squares by studying their
associated hypergraphs. In lazy burning, a set of vertices in a hypergraph is
initially burned, and that burning spreads to neighboring vertices over time
via a specified propagation rule. The lazy burning number is the minimum number
of initially burned vertices that eventually burns all vertices. The
hypergraphs associated with Latin squares include the $n$-uniform hypergraph,
whose vertices and hyperedges correspond to the entries and lines (that is,
sets of rows, columns, or symbols) of the Latin square, respectively, and the
$3$-uniform hypergraph, which has vertices corresponding to the lines of the
Latin square and hyperedges induced by its entries.
  Using sequences of vertices that together form a vertex cover, we show that
for a Latin square of order $n$, the lazy burning number of its $n$-uniform
hypergraph is bounded below by $n^2-3n+3$ and above by $n^2-3n+2 + \lfloor
\log_2 n \rfloor.$ These bounds are shown to be tight using cyclic Latin
squares and powers of intercalates. For the $3$-uniform hypergraph case, we
show that the lazy burning number of Latin squares is one plus its shortest
connected chain of subsquares. We determine the lazy burning number of Latin
square hypergraphs derived from finitely generated groups. We finish with open
problems.
