  We solve the Kato square root problem for bounded measurable perturbations of
subelliptic operators on connected Lie groups. The subelliptic operators are
divergence form operators with complex bounded coefficients, which may have
lower order terms. In this general setting we deduce inhomogeneous estimates.
In case the group is nilpotent and the subelliptic operator is pure second
order, then we prove stronger homogeneous estimates. Furthermore, we prove
Lipschitz stability of the estimates under small perturbations of the
coefficients.
