What is the origin of λ for empty string?
The German Wikipedia claims that $\lambda$ comes from "leer", which means "empty" in German. That seems plausible, as German used to be one of the major languages in mathematics.

Chomsky used $I$ as the empty string (or actually as the identity element for string concatenation) in his early papers. Some people in combinatorics still use $1$ as the empty string, with the same justification.