Diffuse increase in intraepithelial lymphocytes. how likely is it celiac disease? what other tests should be done?

Too vague a question: I trust you are referring to some biopsy findings and thus need to know where the biopsy was obtained. The definitive diagnosis for celiac disease is a small intestinal biopsy. Certain blood tests such as IgA ttg is said to be over 90% sensitive in detecting gluten sensitivity provided that you are not avoiding gluten when the blood sample is obtained.

Blood test: IgA antibody to tissue transglutaminase and/or IgG antibody to deamidated gliadin could be diagnostic.