  We compute the renormalization group running of the Newton constant and the
parameter $\lambda$ in $(3+1)$-dimensional projectable Horava gravity. We use
the background field method expanding around configurations with flat spatial
metric, but non-vanishing shift. This allows us to reduce the number of
interaction vertices and thereby drastically simplify the calculations. The
gauge invariant $\beta$-function of $\lambda$ has two families of zeros,
attractive in the infrared and ultraviolet respectively. They are candidates
for the fixed points of the full renormalization group flow of the theory, once
the $\beta$-functions for the rest of the couplings are added.
