= Solution
For a homogeneous potential contribution of degree $n$, the scalar <virial theorem> follows from the moment of inertia identity $\tfrac12\ddot I=2K-\sum_i\mathbf r_i\cdot\nabla_iU$. Time averaging in equilibrium gives $2K=nU$. Gravitational self-energy has degree $-1$, whereas $U_\Lambda$ has degree $2$. Apply the theorem to the sum of the two contributions:
$$
\boxed{2K_v=-U_{G,v}+2U_{\Lambda,v},\qquad
2K_v+U_{G,v}-2U_{\Lambda,v}=0.}
$$
With the uniform-sphere expressions this is
$$
K_v=\frac{3GM^2}{10r_v}-\frac{\Lambda Mr_v^2}{10}.
$$
The cosmological-constant force is repulsive, so its virial contribution reduces the kinetic support required at a fixed radius. One must not apply the inverse-radius gravitational relation to the whole potential: the two terms have different homogeneity degrees.
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