Since you give no hardware or OS information, I can only give you general information in return.
If your update occurred with a Mint Update, then reverting back to Firefox 18.1 will be difficult, because on your next Mint Update, you will again be faced with Firefox 18.2. If your repositories include Iceweasel from the Debian sources, you could try reverting to that. Iceweasel is presently at 10.0.12, which should work fine with your copy of LastPass, and is the Debian, non-branded version of Firefox with backported security updates.
Or you could temporarily use Chrome/Chromium browser or Opera with LastPass until LastPass is updated to work with Firefox 18.2
LMDE Mate 64-bit, LM16 Mate 64-bit
Debian Xfce 64-bit, Xubuntu 13.10 64-bit, Xubuntu Trusty Tahr 64-bit, Antergos Xfce 64-bit, PCLinuxOS LXDE 64-bit