It depends on what years of the LSJ you are interested in. The MSU Libraries has online versions of LSJ issues going back to 1999, so you can search those for keywords the same way you would search an e-book.
For older issues, you'll need to use either a print or card catalog index. These work like encyclopedias--topics are listed in alphabetical order, and each one has a list of the LSJ articles that talk about it. The MSU Libraries has print indices (which are bound books) for the years 1989-1995, and a card catalog index for LSJ issues published between January 1975 and May 1985. (This card catalog lives behind the Reference Desk on the library's first floor--if you ask the librarian behind the desk, he or she will help you use it). The Library of Michigan owns bound print indices from 1988-1990.