@zoemacuser
If "Menu -> settings -> websites -> Flash -> Allow sites to run Flash" is set, you don't have to do anything and the Flash object at https://www.lexulous.com/live/playboard/ will just load.
If you have Flash set to "Ask first before allowing sites to run Flash (recommended)", the Flash object will be replaced with a placeholder (the puzzle piece) where you click it and choose to allow Flash for the site. In this case, it'll add https://www.lexulous.com:443 to the Flash exception list and set it to "Allow". From then on, it'll just work.
That's of course if you went to https://get.adobe.com/flashplayer/ in Opera and downloaded and installed Flash.
If that doesn't work for you, I'd close down Opera and rename the "Preferences" file in the profile folder. See opera://about for the location. If it works then, you know it's something messed up in that file and we can investigate further. If it still doesn't work, close down Opera and rename the whole profile folder just to see if it works then. If it does, you at least know it's an issue in your profile somewhere. After you're done testing, you can revert things back if you want.
If even a fresh profile doesn't help, I'd download the Opera installer, launch it, click "options", set "install path" to your existing opera program files folder and choose to upgrade. That should fix any program file corruption.
If that doesn't do the trick and the PPAPI version of Flash is really installed, I would think it's something outside of Opera that's intefering or you're running Opera with Sandboxie.