Let $\mathrm{\Omega }$ be an exterior Lipschitz domain in ${\mathbb{R}}^2$. It is proved that the Helmholtz decomposition of the vector fields in $L_p(\mathrm{\Omega };{\mathbb{R}}^2)$ exists if $p$ satisfies $|1/p-1/2|<1/4+\epsilon$ with some constant $\epsilon =\epsilon (\mathrm{\Omega })\in (0,1/4]$, where it is allowed to take $\epsilon =1/4$ if $\mathrm{\partial }\mathrm{\Omega }\in C^1$.