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For $\textrm{SL}(n,\mathbb{R})$ ($n\geq3$), $\textrm{SO}(n+1,n)$ ($n\geq2$),$\textrm{Sp}(2n,\mathbb{R})$ ($n\geq2$) and for the adjoint real split form ofthe exceptional group $\textrm{G}_2$, we exhibit non-uniform lattices in whichwe construct thin Hitchin representations by arithmetic methods. Theserepresentations give infinitely many orbits under the action of the mappingclass group (except maybe for $\textrm{G}_2$). In particular, we show that when$p\neq2$ is prime every non-uniform lattice of $\mathrm{SL}(p,\mathbb{R})$contains thin Hitchin representations.

Zariski-dense surface groups in non-uniform lattices of split real Lie groups