|Images are copyright to Jess Booth of Desert Wind Hounds, and are used with permission.|
Lilly (full name Toumlilt) is an Azawakh, though a fairly unusually colored one. The majority of Azawakhs seen in the Western world are in the Irish white range, while Lilly is very white indeed. This coloration, along with numerous others that are not allowed in the FCI standard, are known in the breed's area of origin but rarely seen outside of Africa due to color restrictions by the current main registry: the FCI. If you're curious to see her as a puppy, there are numerous pictures. Her parents (father Fasiqqi: one, two, three; mother Tiraout: one, two) are within the normal range of what is considered typical for a Western Azawakh. So, on to her genotype.
Lilly is a sable. Though it is difficult to see, she does have a faint trace of black hairs that is especially noticeable as a puppy. It is typical for sables to fade with age, especially clear sables as Lilly and her parents appear to be. Though some other forms of the Agouti locus do appear in the breed, especially in the area of origin, they are not overtly common. I suspect that Lilly is AyAy sable.
As for the intensity of the red for Lilly, it is moderate to moderately pale. I suspect that the most likely genotype for her is cchcch moderate red. In Azawakhs, this is commonly referred to as fawn.
The only other gene that can be known to go into her coloration is on the Spotting locus. On one side, Lilly appears to be extreme white, and on the other she appears more piebald. Since there is some influence in the amount of white in heterozygous individuals, I suspect that Lilly is most likely spsw piebald carrying extreme white piebald.
So, that would be AyAy cchcch spsw or moderately extreme white piebald fawn sable.