(Software) Process:
A serious of steps designed to produce software.
(Software) Methodology:The combination (or set) of
philosophy, process, customs, and culture, used to produce software.
Lifecycle:
I have seen multiple definitions. They both basically say: "The series of stages/steps of a software project from inception until completion." The differ on "inception" and "completion." "Inception" can be anywhere form "I've got an idea for a new product" to "engineering takes charge of creating it;" and "completion" can be anywhere from "release" to "not only is the product no longer supported, we don't even support the migration tools, anymore."
--Mark