Try to look past the colour/pattern (no colour for white) & see all of your birds as Pearl Grey! For the white male (father); he could have other genes that modify his colour from Pearl Grey that we can't see, but he also has from my understanding two doses of an incompletely dominant gene (W/W) which either inhibits pigment production, or prevents the pigments produced from getting into the feather, hence a white bird. In one dose (W/w+), the gene for white inhibits pigmentation in some areas of the bird (possibly quite variable), hence the pied pattern of all your keets because they all inherited one dose of W from the father! We don't seem to have the same gene here in Oz, although we do have pied patterned birds.
The lavender female is lavender due to a recessive diluting mutation in pure form (l/l) which reduces the amount of dark pigment getting into the feather, so darker grey (eg Pearl Grey, Royal Blue) is reduced to lighter blue, ie, lavender. The other female (really have no idea about her colour) very possibly has lavender plus another modifying factor, maybe that for buff/dun for example, plus she doesn't have the pearling, so add two doses of recessive m/m.
Now why all Grey Keets? For the keets to be other then Grey they need to inherit other modifyers that will "modify" colour/patternof the Pearl Grey! If the modifying factor is a recessive, then they will need two doses, except if the recessive gene on the Z chromosome, in which case females only require the one (because females only have one Z chromosome). In your instance, it doesn't appear that your white male is carrying hidden recessive lavender because if he were carrying one dose only then approx 50% progeny produced from the white male & the lavender hen would be lavender. The same could be said for the other hen, ie, whatever factor/s have produced her colour are likely recessive, & the male doesn't carry them!
Remember, we start with a clean slate, ie, Pearl Grey bird, & other modifying factors are added to produce the colour/pattern we end up with