You sure can...
From the web:
You can edit entries in your own journal at
When logged in, you can also edit any entry you created, by going to the "Read Comments" or "Post Comments" page for that entry. Near the top of the page you should see a toolbar with several buttons on it. Clicking the Edit Entry button (the one with the blue pencil icon) takes you to a page where you can edit your entry. If you want to edit a post that you made in a community, you will have to do it this way.
From the Windows Client:
To edit your most recent entry - choose Live Journal - edit last entry (Ctrl-L) - make any changes that you would like to make - then choose ok - your entry has now been updated.
To edit events posted before the most recent entry - choose Live Journal - View History (Ctrl-H) - select the date that your entry was made - Select the entry that you would like to edit - make any changes that you would like to make - the choose ok - your entry has now been updated.
If you have not yet downloaded the client you may do so at http://www.livejournal.com/download/
Backdated entries can be edited in the same ways described above, but they might not show up on your journal page, nor anyone's friends pages. You can find these entries by searching your calendar page, or by entering the entry's date on the editjournal.bml page given above.