This is just the basics as there's enough information about camshaft design to fill several college texts and I'm not about to torture anyone ;-)
Camlobes generally look like an egg, and has a rounder, fat end and a pointy, narrow end.
The fat round end allows the lifter, and in turn the pushrod, rocker and valve, to be in a closed position.
The narrower, pointy end is the end that opens the valve, because it pushes the lifter up, which pushes the rocker "over", and pushes the valve down. This pointy end is called a lobe.
Length of the lobe influences lift, which is how far the valve opens.
The width of the lobe influences duration or how long the valve is open.
The leading slope of the lobe infliuences open rate, i.e. how fast the valve opens.
The trailing slope of the lobe influences closing rate, i.e. how fast the valve closes.
For the most power possible for a given engine, you idealistically want the valve to open fast, stay open a long time, and close quickly.
In reality there are some issues that prevent engineers from designing camshafts that open and close valves nearly instantly and keeping them open a very long time.
Opening valves too fast wears the leading slope of the lobe very quickly, and also applies enough force on the lifter laterally so that it starts to grind into its bore, eventually allowing the lifter to move sideways in addition to up and down. Once these types of wears start to be noticable (about 0.003 inches) the wear starts to accelerate. Crying to close them too fast can result in a "float" condition where the lifter doesn't drop down fast enough to follow the trailing profile, and when it lands, it "bangs" onto the camlobe and after time that starts to wear into both the lifter and the camlobe.
The faster you want to open a valve, the weaker the valve spring must be, and this adds to the float problem on the trailing side of the lobe.
If you regrind the cam and make the lobe smaller and fatter, you will alleviate in part a lot of these mechanical issues - however with a shorter cam profile the valve won't open that far and that introduces yet another problem. The way to solve this (generally) is to increase the rocker arm ratio, so that the part of the rocker that's pushed up by the lifter and pushrod is much shorter than the side of the arm that pushes the valve down.
Increasing the rocker arm ratio too much and the rocker arm material needs to be stronger than stock. Also, the longer the arm the more wear will occur between the top of the valve stem and the point it contacts the rocker arm, because the laterial sliding motion is increased with a longer rocker arm. Not by much but with power of the valve springs the friction that occurs at that tiny little point is quite significant. One "trick" is to insert a roller into the rocker arm where it rubs on the top of the valve stem, however then the weak link becomes the pin that goes through the roller itself. One could do some math and quickly discover on a lawnmower engine doing 3600 RPM that wear point between the rocker and the valve stem is enduring about 2000psi of force, 600 times a second.
Also, by making the radius of the fat part of the lobe smaller in diameter you're allowing the lifter to sit further down in the bore, and depending on the engine block design that may increase the opportunity for lateral movement of the lifter. I personally would compensate for this by using longer lifters, so the original, OEM measurement of shrouded lifter body (the minimum length of the lifter that's always in the lifter bore no matter what) is retained. I don't know what kind of lifters lawnmower engines use, but if they're solid lifters they're not difficult to make at all on a lathe. Just use a quality iron or 4340N.
Now, grinding your own cam lobe or reshaping an existing one is not a trivial task that any of us could do accurately with an angle grinder and a vice. The cross-section of the lobe, meaning the part that the lifter rides on, has to be perpendicular to the length of the camshaft, within 0.0002 degrees. That's less than 1/1000 of an inch for an error margin.
"Back in the day" us racers would pay good money for *our* custom profiles to be made by Crane, Comp Cams, Isky, and others because we didn't have the millions necessary to buy a LeBlanc camshaft grinding machine.
Now, with somewhat affordable CNC equipment being available, you can in fact grind your own camshaft, but you will be putting a lot of effort into setting up the tooling correctly.
What you do is machine the lobe (via a CNC milling machine) out rough with a small diameter, high speed cutter, with the camshaft rotating between two centers on the x-y table. One end is a dead center and the other end is a CNC controlled, indexed rotary table. Once the rough shaping is complete, then you replace the small diameter cutter with a grinding tool and use a different CNC program that takes off the final dimensions for a truly precise cam lobe.