If you are using an airlock, then the headspace should be CO2 and keep you safe from oxidation (not indefinitely, but a while). I think the most important variable is ensuring that yeast is present in whatever container you choose to lager your beer. Obviously, if you leave it on the primary, then there is plenty of yeast. However, if you are transferring to a keg or secondary carboy to lager, make sure you transfer the beer before you crash cool to lager temps. This way, some yeast makes it over into your new lager vessel.