In these sentences the word "lassen" has different subjects:
"lass" (du)
"lasst" (ihr)
You can say as well:
"Lassen wir uns ..." - "Let us..." (the same meaning, subject "wir")
"Lassen Sie uns..." - may be seen as a request, for example children ask the teacher to let them go somewhere
To understand sentences like that better, I would recommend revision of imperative and the word "lassen" (which has so many meanings in German). If you'd like some help with that, I'd be happy to assist you. Feel free to look at my teaching profile or send me a message.