How can I diagnose a power loss problem with a lawn mower?
I believe you do have a carburation problem.  I have several Stihl 2 stroke tools and every time I have a "hard to start" or "loss of power", etc. it's been the carb.  Fortunately they are only about $30 for a replacement.   Every time the replacement carb fixed the problem.   Not knowing the specific make/model of your lawnmower if a replacement is as simple as my 2 stroke Stihl units.   In your case, if you are familiar with carbs, I'd try disassembling it, clean it and put it back together and try.  There are often rubber parts that break, get torn, or get stiff and need to be replaced.  If practical, I'd try a new carb, depending upon how old the mower is.