There is a lot going on in this book -- lots of plot twists and turns, but here is the basic story.
Artemis Senior has been kidnapped and Artemis Jr wants to get him back. The LEP needs Artemis's help so that they can break a smuggling ring run by the goblins. Artemis offers to help in return for the LEP's help in getting his father back.
While Artemis, Butler, Holly and Julius Root are trying to get Artemis Sr. Briar Cudgeon (with help from Opal Koboi) takes over LEP headquarters, locks Foaly in his Operations Booth, and makes it look as if Foaly is leading a revolt against the LEP.
In order to end that, Artemis and the rest go to Los Angeles and capture Mulch Diggums. They get him to tunnel into Koboi's lab and return control of all of LEP's weapons to LEP.
Once they have done that, they go back and complete the rescue of Artemis Senior.