Lets count后面可以跟很多东西，比如lets count to 10(数到10)、lets count our blessings(数数我们的福气)等等。
所以具体要看上下文来确定跟什么内容。
No, "let's count to three" is correct. It is a common phrase used to suggest that a group of people count together to achieve a common goal or to synchronize an action.
Let's go是祈使句，go是原形不能加ing而变成going。但go后面可以接动名词或动词不定式的，用以表达go具体的行为的。如，
Let's go swimming 让我们去游泳吧。
Let's go fishing 我们去钓鱼吧！
Let's go shopping.我们去购物。
Let's go to see a movie.
我们去看电影。