Yes, you can access the Los Angeles Times online through the library! There are several different databases that make it available to you. It's a little confusing because different databases provide access to the LA Times at different time periods.
To Browse Current Issues
If you're interested in reading current LA Times news, you can access it directly through the database Global Newsstream. This page always defaults to the most recently published issue and you can search by specific issue/date as far back as 1996.
To Search Recent and Historical News
If you want to do a keyword search within the LA Times from as far back as 1985, go to the LA Times OneSearch record. Under "View Online," there are several databases listed (hyperlinked in blue) and beneath the database name will be a date range. Click on the database for the date range you wish you search.
You'll notice that Global Newsstream offers three options, and there is some overlap on dates. Global Newsstream has almost all issues of the LA Times from 1985 to present.
ProQuest Historical Newspapers: Los Angeles Times has most issues of the LA Times from October 23, 1886 to December 31, 1995.