Thank you, gentlemen, for your responses. They all helped. I'm finding out Lawn Boys can be confusing.
I finally stumbled on a site which shows Lawn Boy used three carbs on the F100 engine. No wonder local shops were having a hard time figuring it out. The site is
https://lookup3.toro.com/ttcGateway/acrobat/manuals/lball.html. Page 4-34 titled "F Series Carburetor Identification" shows the three carbs. The speed control lever I need looks like the one in the middle picture. Page 4-51 deals with the governor, but it has the best picture of my carb and the speed control lever I need. I'd post an actual pic of mine, but I can't get one.
I can't find the part number for for the speed control lever I need. The suggested speed control lever number 609631 is close, but it looks like that one is for the "early model" carb. My carb appears to be a "later model." My mower is model 5247, serial number 9510868, F100 engine.
Do any of you fellows know the part number for the speed control lever for my carb? Can you direct me to a source for one? This has myself and two local shops stumped. An old Lawn Boy dealer told me it's an obsolete part, and they don't know where to locate one.
Thanks, again, to everyone for helpful responses.