Would this mean to eagerly anticipate something, as in licking one's lips?
Yes, but primarily it refers to tasty food anticipation.
to not lift a finger?
That strikes me as having virtually the same meaning then. If a person is not going to budge an inch,
Not quite. This inch idiom suggests obstinacy, stubborness. While finger idiom means the refusal to take action. e..g, I won`t bend a finger to defend you, you little rascal!
Another one: My mum often said (in imperative style but addressing nobody in particular): Be wise and write poems