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Norops conspersus
garmani and equestris, going by Powell and Henderson 2012. I can send you the paper if you shoot me and email john-phillips@utulsa.edu
@John What are the other two for "Grand Cayman", I only found 3 on http://www.caribherp.org
Anolis carolinensis, A. sagrei and A. conspersus (Norops conspersus) are the anoles found on Grand Cayman. I agree that it looks most like a drab Anolis conspersus, perhaps a female.
Marinus is correct. Out of the 5 anoles known for Grand Cayman, this is the only one that comes close. Looks like you have a female.