Luke 14:1-5

Luke 14:1 (KJB)
And it came to pass, as he went into the house of one of the chief Pharisees to eat bread on the sabbath day, that they watched him.

Here Jesus was still in the area of Galilee and Peraea and one of the chief Pharisees in that area had invited Him. If you notice, it was on the Sabbath day when the invitation came which meant that they were once again making an attempt to trap Jesus concerning the Sabbath. It seems that they believed if they were going to trap Him, it would be based on some violation of the Sabbath.

Luke 14:2 (KJB)
And, behold, there was a certain man before him which had the dropsy.

The dropsy was a condition where a person had an excess buildup of fluids in the connective tissues or cavities of the body. It basically manifested itself in swelling or distension, which was an enlargement of a joint due to internal pressure. If this man had such a condition, he would never have been invited to the house of a Pharisee on a normal occasion. He was no doubt invited to see if Jesus would heal him on the Sabbath day. It was another trap.

Luke 14:3 (KJB)
And Jesus answering spake unto the lawyers and Pharisees, saying, Is it lawful to heal on the sabbath day?

Here is another set up to see what Jesus would do on the sabbath. They knew that He would have compassion on someone with a serious medical condition and this manís condition meant nothing to the scribes and Pharisees. They wanted to see if Jesus would heal on the sabbath day. If He did, then they would also have enough witnesses to bring Him before the Sanhedrin and accuse Him of violating the sabbath. Jesus asked them straight out, is it lawful to heal on the Sabbath Day? They realized that if a personís condition was so that his life was in peril, then medical help would be allowed on the sabbath but this manís condition was not life threatening as of that point, so it was basically a set up.

Luke 14:4 (KJB)
And they held their peace. And he took him, and healed him, and let him go;

They held their peace because they refused to acknowledge that the law did not forbid such a healing. If they would have answered, they would have removed the only thing they planned to use against the Lord. However, their silence also worked in the opposite way. If they could not raise an objection before the healing, then they would not be able to raise an objection afterward. They literally defeated themselves. Jesus allowed the man to leave because He knew that the only reason He was allowed in to that meal was for the purpose of trapping Jesus and He did not want that man in the middle of a theological debate.

Luke 14:5 (KJB)
And answered them, saying, Which of you shall have an ass or an ox fallen into a pit, and will not straightway pull him out on the sabbath day?

Jesus then asks them a question which would focus on compassion for animals. If it was the Sabbath day and one of them had an ox or a donkey which fell into a ditch, would they leave them there until the following day or would they make an attempt to pull them out of the ditch so they would have no further injuries. Jesus had used this same argument previously except it was to loose the animals to feed and water them. He then waited for them to answer.