What does Luke 11:37 mean?

Despite the Pharisees' antagonistic relationship with Jesus, they occasionally invite Him to their homes (Luke 7:36). As in Luke 7:36–50, the fact that they "recline" indicates this is a formal meal. They are lying on couches around a table. Most likely, the doors are open, and people are standing quietly along the walls to hear the conversation.

Later, Pharisees and lawyers will invite Jesus to dine on the Sabbath to see if He will heal a man. They intend to see if He will violate their interpretation of what it means to "do no work" on the holy day. He does, telling the religious leaders that if they would save an animal, He is justified in healing a man (Luke 14:1–6). Considering that situation, it's possible this Pharisee has invited Jesus to "provoke him to speak about many things…to catch him in something he might say" (Luke 11:53–54) as they will in the week before the crucifixion (Luke 20:19–20). Of course, it could have also been motivated by a desire for the prestige of hosting a notable person, genuine hospitality, or for further conversation, whether in the cultural tradition or from true curiosity about the things Jesus said.

The religious leaders get their wish but not in a way they expect. Jesus proceeds to describe Pharisees as "unmarked graves," "full of greed and wickedness" (Luke 11:39, 44). When the lawyers respond, Jesus tells them they follow the traditions of their fathers who killed God's prophets (Luke 11:45–52).