Lepista nuda is a widely used synonym that is falling into disfavor. However, as of June 2007 according to Index Fungorum both names are valid, so I’m leaving it that way.
The primary issue here is an on going debate about the correct type for the genus Clitocybe. Some, including Singer, take the type to be C. gibba. However, the growing opinion (and I believe at this point the majority of experts) takes C. nebularis to be the type. If you take C. nebularis to be the type then Lepista is becomes a deprecated synonym of Clitocybe and Clitocybe nuda is the correct name for this species.
Very similar to Clitocybe glaucocana. According to Denise Gregory’s key to Clitocybe in California, they can be distinguished based on the cap color when young. In the case of C. nuda they should be deep violet or purple. C. glaucocana, on the other hand, is light violaceous, light blue or faintly purple when young. It would be nice to know if there are other reliable ways to distinguish between the two species.
As a side note the type species for Lepista is L. panaeolus which from photos looks pretty similar to L. nuda. Singer separates Lepista from Clitocybe on the basis of the smoothness of the spores(!). I have heard that other separate them based on the spore color (pink for Lepista, white for Clitocybe). Macroscopically L. nuda also seems like it should be closely related to Clitocybe brunneocephala, but that species has never been transfered to Lepista as far as I know.