Neutral for the ritual, he's aligning either with the Beast +/- Earth Spirit (depending on how Peridot/Foster/Miko's investigation shakes out).

That being said, he's supporting efforts are underway to weaken the Rose Queen (helped Yuya with the rose spell, being dragged in RQ shenanigans by Rita probably) and has killed at least one Winter Court changeling trying to go for Childermass. At some point last week he talked Zangetsu into beating up some Circle mooks and kicked the ass of some minor demons going after a ghost, so basically the only people Lambert hasn't aggro'd some way are the angels...