The OP's question is a variation of this question, with a different start point. The answer, therefore, is very similar:
Its often conjectured that the observable universe will asymptote to a de Sitter state (dark energy only, no matter, flat universe).
It is well known that the de Sitter characteristic length $l_\Lambda$ (i.e. future cosmic event horizon radius) is related to the cosmological constant $\Lambda$ (dimensions $L^{-2}$):
\begin{equation} {\Lambda} = \frac{3}{l_\Lambda^2} \end{equation}
That
Also, in a dS state, the future Hubble Horizon equals the cosmic event horizon, so:
\begin{equation}
{l_\Lambda} = \frac{c}{H(\infty)}
\end{equation}
That is the OP's $1/R^2$ relationship, but its a relation to (also pointed out via the Hubble parameter by the other answers); the $R$ is the future de Sitter cosmic event horizon radius, which is a fixed number. At the present time, the radius of the observable Universe is around 2.9 times the future dS CEH radius.
TLDR: $\Lambda$ is related to the future cosmic event horizon radius, which is fixed. As an energy density (i.e. vacuum energy) the cosmological constant remains also fixed over time. The radius of the observable universe, on the other hand, is not fixed.