Dad had an old Gravely that he put an electric starter on when he got too old to pull the strap. He'd turn it forward up on the top of the compression stroke, then hit the button. This would give it two crank rotations to get up to speed for starting. Old machine is still running and gets...
I'd try to relap the valves before doing anything serious. Having the valve sticking open a bit might have messed up the seat to valve contact. Get some lapping compound, probably videos on Youtube on this.
Might check on that gas tank issue. There was/is a recall on a lot of the LB tanks like yours. I checked into it for my leaky F engine tank and it was covered but I would have had to take it to a dealer for replacement. Can't imagine any mower dealer these days fooling with a 40 year old Lawn...
Basic Briggs flathead Kool Bore.. I'd guess the cylinder is shot. New rings might help it but this is getting pretty common these days. The chrome plating on the piston wears and the bare aluminum surfaces rubbing together creates a mess. Hope I'm wrong but you'll have to pull the head and check.
Bought the wife a new HP desk top with Win 10 a year ago. Hear nothing but complaints and all I get done is trying to clean it out so it will work decent for a couple weeks. My Chromebook works flawless and this old Gateway with Win8 also works pretty decent.
Does this motor have a sleeved bore? Briggs&Stratton calls this an I/C - industrial commercial - engine. If it is sleeved the standard oil is probably ok. I'd still run the Kohler SH/SJ rated oil, or an additive.
I suspect this has a brushless motor. These have a lot of electronics to power and control the motor and are highly stressed. One component goes south and it's done. Pretty expensive mower and most reviews are basically negative. Ouch.
The old LB mowers with alloy deck and good wheels that run seem to bring about $100 in season around here. Real handy for trimming but not used for serious mowing. Might post a couple pictures and the Lawn Boy enthusiasts on here can pin-point the year I suspect.