In the Heisenberg group ${\mathbb{H}}^n$ and for exponents $2\le q\le 4$, the local Lipschitz ($C^{0,1}$) regularity is demonstrated for weak solutions to a non-homogeneous highly degenerate q-Laplace equation of the form $-{\sum }_{i=1}^{2n}{X}_i\left({\lambda }_i(Xu)X_{i}u\right)=g(x)$, where ${\lambda }_i(z)={(z_i^2+z_{i+n}^2)}^{{\displaystyle \frac{q-2}{2}}}$ for $i=1,\dots ,n$ and ${\lambda }_i(z)={(z_i^2+z_{i-n}^2)}^{{\displaystyle \frac{q-2}{2}}}$ for $i=n+1,\dots ,2n$. Our approach draws heavily on the work of X. Zhong. However, owing to technical limitations, the regularity of weak solutions for $1<q<2$ and $4<q<\infty$ remains unclear.