Local automorphisms of nilpotent algebras of matrices of small orders

Let $K$ be an associative commutative ring with identity and let $R$ be the algebra of lower niltriangular $n\times n$-matrices over $K$. For $n=3$ we prove that local automorphisms and Lie ones of the algebra $R$ generate all local Lie automorphisms of the latter. For the case when $K$ is a field and $n=4$ we describe local automorphisms and local derivations of the algebra $R$, as well as its local Lie automorphisms.