  We analyze different claims on the role of the coupling constant lambda in
so-called lambda-R models, a minimal generalization of general relativity
inspired by Horava-Lifshitz gravity. The dimensionless parameter lambda appears
in the kinetic term of the Einstein-Hilbert action, leading to a one-parameter
family of classical theories. Performing a canonical constraint analysis for
closed spatial hypersurfaces, we obtain a result analogous to that of Bellorin
and Restuccia, who showed that all non-projectable lambda-R models are
equivalent to general relativity in the asymptotically flat case. However, the
tertiary constraint present for closed boundary conditions assumes a more
general form. We juxtapose this with an earlier finding by Giulini and Kiefer,
who ruled out a range of lambda-R models by a physical, cosmological argument.
We show that their analysis can be interpreted consistently within the
projectable sector of Horava-Lifshitz gravity, thus resolving the apparent
contradiction.
