I am looking for literature references for the notion of a 'lax' monad (or triple), and lax algebras over such, in the context of 2-categories--the definition being that the usual diagrams commute only up to a 2-cell. Can anyone suggest good references?

Some good old references are: M. Barr "Relational algebras" SLNM 137 (1970) 39-55 M. Bunge, "Coherent extensions and relational algebras" Transactions AMS around 1974. G.M. Kelly & R. Street, "Review of the elements of 2-categories" SLNM 420 (1974) 75-103. --Ross