“the prophets.” The context tells us these are the false prophets. We can see why Jeremiah felt so alone and wept for the people. He heard from God and was not confused, but the people would have been confused by all the false voices. Furthermore, as we see in the fact that Jeremiah was beaten, put in stocks, etc., that these false prophets came against Jeremiah personally.
“lasting.” The Hebrew word has many meanings, including “firm, faithful, sure, reliable, stable, continuing, true, etc.” The versions differ as to which meaning to chose for the best fit here. To the people listening to the false prophets, the word would indicate all of those things, and thus the false prophets were saying there would be a true, firm, reliable, lasting, stable state of wellbeing in Judah. They were very wrong.
“peace and prosperity.” The Hebrew word “shalom” means more than “peace,” it means wellbeing, wholeness. In this context of conflict and war with the Babylonians, “peace” is too narrow a meaning, The prophets were foretelling “shalom,” peace and prosperity.