^^ Anney, that's honestly not really accurate. There are, of course, situations where "Let's go!" means something like "Hurry up, already!" (especially when a parent is talking to their child). But, on a whole, the contraction changes nothing. The only difference between, say, "Let's eat" and "Let us eat" is that the latter is less casual.
The reason "Let's go!" sounds like an order, in certain circumstances, is because that particular phrase is often used in military settings. to indicate you will together charge the enemy, or start an operation or some such (like "Let's go! Today, gentlemen! Today!"). So, when a parent says "Let's go!" to a child (with the emphasis on 'go') it will have a similar connotation. But "Let's go!", in and by itself, is no more than a contraction. Like (casual):
"Wanna catch a movie?"
"Sure. Let's go!"
There's no order implied there. Nor a request. It just means "Let us go."