The open source plugins availables are incompatible with sun java or lack of functionalities.
On the other hand, Flash plugin work out of box in ubuntu hardy 64 bits.
After do a little research i found a simple method to get logmein working.
We will install a special version of swiftweasel, running 32 bits code inside a 64 bits OS.
1)Double check universe and multiverse repos are enabled, if dont just goto System -> Adminstration -> Software sources and enable them.
2) Donwload that script, unzip and runit. More detailed instructions from the author here.
3) Choice your distro.
4) Choice internet navigator.
5) Installing progress.
6) Want install Flash? Is not a needed step, ubuntu install it rigth.
7) Install Java? Is required for use logmein.
8) Install Mplayer Plugin? Recomended.
9) The install scripts ask for your username
10) Done. We have a 32 bits firefox running on our 64 bits system.
11) Install the logmein plugin for firefox.
Get it on the logmein web, labs section, aqui . Dont install the deb file, just save that.
Open a terminal , go to the place you save the deb file and type::
sudo dpkg -i --force-architecture logmein-client_1.0.387-1_i386.deb
Done, now you can enjoy using logmein in your 64 bits system.
Namaste