Nontrivial semidirect product of cyclic Lie ring of even order and cyclic Lie ring of order two

Definition
Let $$n$$ be a natural number. This Lie ring defined in terms of $$n$$ has order $$4n$$ and is defined as;

$$L_{4n} := \langle a,x \mid (2n)a = 2x = 0, [a,x] = na \rangle$$

When $$n$$ is odd, this is a solvable Lie ring that is not nilpotent. When $$n$$ is even, this is a nilpotent Lie ring; in fact, it is a Lie ring of nilpotency class two. When $$n$$ is a multiple of $$2$$, it has a Lie group.