If you want to buy a new lawn mower, you can go down to your local big box retailer and find that most of the available options are probably battery electric mowers.
But, not that many years ago, electric mowers kinda sucked. The few choices you had were all corded but more importantly, they were cheaply built and lacked power. They also had none of the features of gas mowers, like being self propelled. After wearing out two of them within a couple years I thought, "This is cannot be that hard. I bet I can build a better electric mower."
A rotary lawn mower is pretty basic. Engine spins blade, blade cuts grass. That's pretty much it. If you wanted to "electrify" a gas mower, you would need a motor that could supply sufficient torque and keep the blade speed within the right range.
I picked up a 2 HP induction motor and mounted it on a frame which would basically serve as a drop-in replacement for the engine. I also built a switch which connected to the dead-man switch/engine brake bar, allowing the motor to be turned on and off.
I quickly learned the importance of selecting the right mower to convert. My first attempt was a Troy Bilt front wheel drive, which did not work well. Electric motors are heavy and the induction motor was substantially heavier than the engine it was replacing. The front wheel drive mechanism was not designed to handle the extra weight and it made navigating difficult.
My next attempt was with a John Deere rear wheel drive. That one was a winner. I ended up building a really solid electric mower that performs nearly on par with a gas mower. The only downside is that it requires a heavy extension cord due to the power draw but once you get used to the cord it's not that bad.
I used this thing for probably 8 years without any problems and no maintenance besides sharpening the blade and greasing the bearings about once a year. I replaced it with a cordless mower last summer but I'm not getting rid of it. It's in my shop getting a badly needed rebuild and a safety upgrade (adding an electric brake). It'll be back on the job, at least part time, whenever I get a chance to put it back together.
More photos in the comments.