  We use observational data from Type Ia Supernovae (SNIa), Baryon Acoustic
Oscillations (BAO), and Cosmic Microwave Background (CMB), along with
requirements of Big Bang Nucleosynthesis (BBN), to constrain the running
parameter $\lambda$ of Horava-Lifshitz gravity, which determines the flow
between the Ultra-Violet and the Infra-Red. We consider both the detailed and
non-detailed balance versions of the gravitational sector, and we include the
matter and radiation sectors. Allowing for variation of all the parameters of
the theory, we construct the likelihood contours and we conclude that in
$1\sigma$ confidence $\lambda$ is restricted to $|\lambda-1|\lesssim0.02$,
while its best fit value is $|\lambda_{b.f}-1|\approx0.002$.
  Although this observational analysis restricts the running parameter
$\lambda$ very close to its IR value 1, it does not enlighten the discussion
about the theory's possible conceptual and theoretical problems.
