My intuition is that there's no difference between "Let's go further" (which I interpret to mean "Let's go {on / forward}" and "Let's go forth" (which I interpret to mean "Let's go {on / forward}". "Forth" means "forward", and that's what you meant when you said "further". The only difference I can see is one of style. "To go forth" is older that "to go further".
Watch out for that skunked term "Native American". It literally means "born in America", but, like "gay", which used to mean only "happy" or "joyous", has acquired a political meaning ("homosexual") that supersedes its traditional denotation. Likewise, "Native American" is now a political term that means "aboriginal American". I never use the term myself, and I'm not certain that Malvolio's assertion is correct that it applies to all the people who were here before the Europeans conquered what are now called North and South America. To most USA Americans, only people who are citizens of the USA are what is commonly called "American". To some politically peevish pedants, however, almost everyone living in the western hemisphere is "one kind of American or another". Nonsense. Nobody going to America is going to Brazil, and nobody going to Brazil is going to America. While Brazilians are without doubt South Americans, they are not Americans in the same way as USA Americans who say, when asked "What's your nationality?", "American". But this is politics as well as English usage and a pointless -- because fruitless -- discussion to get involved in. It's one of those "You're either a believer or a heretic" propositions. It's a matter of stipulation and pigheadedness.