This is the question: Find a regular grammar for the language

L $=\{$anbm : n $+$ m is odd$\}$

This is the given answer:

EE $->$ aOE$|$bEO$,$

OE $->$ aEE$|$bOO$|\backslash$lambda $,$

OO $->$ bEO,

EO $->$ bOO$|\backslash$lambda

Please walk me through the steps required to get this answer. I am confused on what Lambda does, as well as the thought process required to get this answer. Thank you.