What is the ruling on saying: "And my Lord is like my friend, He will not abandon me" and "I cannot live without you," and similar phrases?

If the bond of close friendship (khullah) is legitimate, for the sake of Allah, and with righteous people, then there is no harm in swearing that such a close friend will not be abandoned, due to the reward it entails and because a person is influenced by their close friend. The Prophet, peace and blessings be upon him, encouraged us to seek righteous companionship and forbade us from befriending non-believers. However, if the close friendship is illegitimate, such as between a man and a woman, then both are sinful and must sever it. If marriage is possible, they should do so; otherwise, not. As for the second phrase, "And after you, I shall live (no more)," it contains exaggeration, and reality has proven its falsehood.