I suppose that you already know about this? It's LJ apologising for the poor service (most of it not their fault) recently, which is damn good of them.
Basically, if you had a paid account at any time during June, you can claim an extra two weeks OR if you buy six or twelve months of time VERY soon (I think you have a couple of days left), whether it's a new paid account, an upgrade from free to paid, or an extension to an existing paid account, you can claim an extra TWO MONTHS instead (NOT as well!).
The link will tell you what to do. If you're taking the two month option, that won't show up on the Paid Time Reimbursement Page UNTIL your payment has been fully processed - credit cards are nearly instant, PayPal may take a few hours - so don't panic if you pay and the option doesn't show up for a while; just be patient.
And thanks to the lovely episcopus for pointing it out.