Again, King Lemuel is unknown in the Bible and is most likely a non-Israelite. Job is the most well-known non-Israelite in the Old Testament and while Israel was undoubtedly the focus of God's work in the Old Testament, it is not restricted to Israel.
These sayings are actually words taught to him by his mother, and are largely a series of warnings.
The first warning is against chasing after women. You only need to open a newspaper, or look on a news website, to see a fair selection of people who have made fools of themselves with women.
The second warning is against drink. Rulers should not get drunk, for then they may make stupid decisions and many people will be affected by these decisions.Verses 6 and 7 seem to say that the poor and downtrodden should get drunk so they can forget their terrible state. I don't think we should take this as positive advice, but as a commentary on what drink (and in our day drugs as well) do in the social scheme of things. They are seen as a way of escaping the terrible or hopeless life that some have. In the end, they lead only to death.
This little section closes with positive advice, instruction on what rulers are meant to do. This is to speak up and act on behalf of the weak and destitute.