In the United States today, there is an abundance of information available on weather forecasts. If you are reading the paper, watching the news, or listening to the radio, you are likely to encounter predictions being made regarding the weather for the upcoming hours or days. Often these forecasts are accurate, but not always. Even with our impressive advances in technology, mankind is still unable to predict the weather accurately all the time.
Of course, even without technology, simple observations have always been helpful in predicting impending weather. In Jesus' day in Palestine, when a cloud was seen to be rising from the west (i.e., out of the Mediterranean Sea), it was understood that rain was on its way. When the wind blew from the south (from the equator), it would cross the deserts and wilderness and bring distressing heat with it. The Jews in Jesus' day were observant to these truths. They knew when high temperatures or precipitation was coming. However, tragically, they were blind to other observations that were much more significant.
Their hypocrisy was clearly evident to Jesus. They did not "discern this time." In other words, most of the Jews had physical perception regarding the immediate future (i.e., of the weather), but they had no spiritual perception. They understood the physical indicators of the weather but were blind to the spiritual indicators of that time (i.e., the ministries of John the baptizer and Jesus and the prophecies they fulfilled). Surely all should have seen that the signs pointed to Jesus as the Messiah just as a cloud rising from the west pointed to an approaching shower! They had the warnings of both John and Jesus about matters and conditions which were so plain that they should have been able to see them without any warning whatsoever.
On the surface, Luke 12:58,59 is quite similar to Matthew 5:25,26. However, the contexts are much different and so is the specific application. The Jewish religious leaders considered Jesus to be their adversary, and in a very real sense, Jesus is an adversary to those who do not know God and to those who refuse to obey the gospel (cf. II Thess. 1:7-9). According to their own evaluation of Him (as their adversary), Jesus counsels them to come to terms with Him before it is too late! They needed to make peace with Him or else! Whether they realized it or not, they were on their way to the Judge, both individually and as a nation.