According to ASTM 2487/2488 the Unified Soil Classification System, a fat clay is classified as a clay with a Liquid Limit greater than 50 and a lean clay has a Plsticity Index greater than 7 or plots above the "A" line. I hope this helps.
Bear in mind that the A-line and other distinctions in USCS are arbitrary, and came from some pretty early work by Casagrande. The A-line does not effectively divide different types of behavior. One can find some extremely plastic materials (consisting primarily of montmorillonites and other clay minerals) that plot below the line, making them MH rather than CH according to the USCS. We are stuck with the distinctions and the chart as they exist today, but if we really wanted to use them to make distinctions in soil behavior, we would draw them differently, so we do not have material with a PI of 50 and LL of 100 lumped with materials having a PI of 5 and LL of 50. Simply calling material "MH" does not describe the material very well. "CH" is better in that regard.
I wish ASTM and others would abandon the terms "fat clay" and "lean clay," along with "elastic silt," because they don't make sense semantically. "Highly plastic," "high-plasticity," "low-plasticity," etc. are more meaningful, although I admit that those too are code words for "having a high plasticity index," etc.
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