Lavender is not an officially recognized color for Ameraucanas by the APA or the Ameraucana Breeders Association, but there are Ameraucana breeders who are breeding them and working to get them officially recognized.
Olive Eggers are also Easter Eggers. They just happen to be EEs produced by crossing a blue egg layer with a chocolate egg layer. The resulting offspring is an EE that lays olive colored eggs and is referred to as an Olive Egger. There is a good article explaining this at...
You can breed an EE from all of them by crossing them with a blue egg laying breed such as an Ameraucana, Araucana, or Cream Legbar. If you cross them with an EE, the offspring may or may not be a colored egg laying EE. It depends on whether the EE parent gives its blue egg gene or its brown egg...
There is a good article at http://www.the-chicken-chick.com/2011/09/ameraucana-easter-egger-or-araucana.html explaining the difference between an Ameraucana, Araucana, and Easter Egger.