I have been reading conversations like the following: Hey, let's go for a jog this afternoon! Is it correct to only say let's! instead of let's go!?

In the questioner's examples, the sentence means to say product (allows/permits you to) do. Today when it was about time to go home, my english teacher asked me to lead my friends to pray in english. I led them by saying let's pray together! however, my teacher told me that i. Many people use let, let's and lets in conversation what's the difference between them?