Marco Manetti has expanded the 22-page lecture notes from 1999 mentioned in the OP into a 574-page text book: Lie Methods in Deformation Theory (2012).
It is advertised as "being the first book to apply the differential graded Lie approach to deformation theory of complex manifolds".
I have the impression the pdf can be downloaded freely from Springer (but perhaps that functionality is tied to my IP range).
Carlo Beenakker
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