Irony of Curiosity
In many of Lovecraft's stories, the main character is a person who wants a better understanding of events and phenomena in the surrounding world. In "The Outsider" the main character is a child who, frustrated at living alone, attempts to contact other people. In "The Horror at Martin's Beach" it is a ship's captain and several volunteers who attempt to capture a large, unknown creature. In each case, the curious person pays a huge price: the child realizes he is a monstrous beast, and the captain and other volunteers are captured by the strange creature and die by drowning. Herbert West, in seeking to more fully understand and reverse the effects of death, is killed by his own zombies.
Irony of Divinity
The gods created by Lovecraft are not creative or benevolent. The "Old Ones" or "Old Gods" of the Cthulu mythos, or the various strange and powerful extraterrestrial or undersea beings that appear in some of his stories such as the hulking Dagon do not resemble the benevolent creative force like the one in the Judeo-Christian tradition. They do not resemble human beings, they do not have any particular regard for the survival of humanity, and they are not "good". For most people, raised with the mostly benevolent and humanoid gods of the Greek, Roman, or Hindu pantheon, Lovecraft's deities are the exact opposite of what they would otherwise expect.
Irony of Reality
Randolph Carter, who escapes from the Lovecraftian dream world with his life and sanity intact, becomes a very unhappy man because his only happiness and curiosity is in the dream world. Eventually, he concludes that there is no difference between dreams and reality.
Irony of Weakness
Many of the weak, aged, and infirm characters in Lovecraft's writing are not what they appear to be. In "The Terrible Old Man", an apparently weak and feeble old man appears at first to be an ideal target for robbers, but kills all three of them.
Irony of Dreams
Most people think of dreams as pleasant, beneficial things. When they say they "dream" of doing this or that, it means they have a desire to experience it. Yet Lovecraftian dreams are often more nightmare-like, consisting of chaotic imagery and hideous, otherworldly creatures. The irony of Lovecraftian dreams is that they are unpleasant and unpredictable, since the normal laws of physics, science, and causality don't necessarily apply.