I usually use the symbol $\varepsilon$ for empty string (empty word or null string). But I know some people use $\lambda$ instead of $\varepsilon$.
I think $\varepsilon$ is derived from the word "Empty". However I don't know what's the origin of $\lambda$.
In automata theory, there is the epsilon transition of automata, and it's also said to be the lambda transition. For example, JFLAP software uses $\lambda$ for the label of epsilon transitions by default.
I googled on the origin and searched cs.stackexchange, but I couldn't find. Does anyone know a reference that describes this?