A precise method for relating quite general kinds of metric 3-algebras with metric Lie algebras and their unitary representations will be described. Several special cases of this construction will be highlighted, that apply to certain types of superconformal field theories dual to M2-brane configurations. Recognition of M-theoretic properties in terms of Lie-algebraic data will be noted in passing. Some remarks will be made on the general structure of metric Lie 3-algebras, which describe maximally supersymmetric Bagger-Lambert theories.