Be very careful about using old outboard fuel in a lawnmower, strimmer, chainsaw, etc. 2str outboard oil is not suitable for them. I knackered my strimmer after just occasional use over two years. First thing the dealer said was, 'You've been using outboard fuel, haven't you?' He sees it all the time.
I think outboards must run cooler than other engines and the oil can't cope with higher temperatures.
I would just add some fresh fuel to the older stuff and use it in the outboard. Or, maybe, add small quantities of the old to the new.