I'd approaching a "septic system friendly" path to verbs my slow moving lavatory drain.? ...

Need to know where on earth the pump...
Answers:    Take out the stopper and use a coat hanger bent into a hook to pull up any spike which has gotten caught on the stopper workings.
Lawn mower problems beside the cord?
Simply use a plunger. Sometimes whatever have it clogged can be unclogged by doing this. This is the individual thing I can suggest lacking using Drano or something to break it up.