The primary conflict which drives the action of the novel is that Percy must find and return the stolen master bolt to Zeus, king of the gods. He receives a hero's quest from the oracle at Camp Half-Blood that he must "go west, and face the god who has turned [...] find what was stolen, and see it safely returned" (141).
As Percy accepts this quest and leaves to find Hades and the Underworld, he encounters many dangerous monsters and threats that attempt to deter him from reaching his goal. Percy knows that the stakes are high for him to find and return the bolt, for if he fails at his task, Chiron predicts "western civilization turned into a battleground so big, it will make the Trojan War look like a water-balloon fight" (138).
The main conflict would be that the master bolt had been stolen and Zeus thinks Percy is the main culprit. Why? Well, Zeus and Poseidon have been fighting for centuries, and suddenly Zeus's main weapon, the master bolt, goes missing. A god cannot steal another god's weapon of power, but a mortal hero can. Around the same time, Poseidon openly claims Percy as his son, and Percy was in New York for the Winter Solstice, when the bolt went missing. Zeus believes he has found his thief. Because of this, Percy has to go find the bolt or basically face death.
A subtler conflict would be between Luke and Percy. Ultimately, it is discovered that Luke was the one that placed the lightning bolt with Percy and confesses he is working for Kronos.
The main conflict would be that Percy is trying to come to terms with his father being Poseidon, and that he is accused of stealing the lightning bolt and being tasked to find it.
the main conflict would be the way that percy reacted when he found out that his father is poseidon. also, another conflict would be when percy is accused of stealing the lightning bolt.