Nilpotent Lie algebras of derivations with the center of small corank

Let $\mathbb{K}$ be a field of characteristic zero, $A$ an integral domain over $\mathbb{K}$ with the field of fractions $R=\text{Frac}(A),$ and ${\text{Der}}_{\mathbb{K}}A$ the Lie algebra of all $\mathbb{K}$-derivations on $A$. Let $W(A):=R{\text{Der}}_{\mathbb{K}}A$ and $L$ a nilpotent subalgebra of rank $n$ over $R$ of the Lie algebra $W(A)\mathrm{.}$ We prove that if the center $Z=Z(L)$ is of rank $\ge n-2$ over $R$ and $F=F(L)$ is the field of constants for $L$ in $R,$ then the Lie algebra $FL$ is contained in a locally nilpotent subalgebra of $W(A)$ of rank $n$ over $R$ with a natural basis over the field $R\mathrm{.}$ It is also also proved that the Lie algebra $FL$ can be isomorphically embedded (as an abstract Lie algebra) into the triangular Lie algebra $u_n(F)$ which was studied early by other authors.