Your L-B is very similar to my 10330. Here's its story:
I found this lawn mower in the neighborhood on a walk with the family one night. It was obviously left for dead. It was on an un-mowed empty lot. One of the front wheel adjusters was jammed, making the whole unit set uneven. The intake manifold was loose on the cylinder head; the engine couldn't have run. The self-propelled cable was so out of adjustment that it wasn't self-propelled. And the winning factor -- the blade was sharpened on the TRAILING edge of the blade. This mower couldn't have cut through butter, let alone a lawn of grass.
The 10330 came with a Tecumseh LEV100 4-stroke engine, of 4.5 hp. It sort of ran after I fixed many of the issues above. It ran real lean, though. It ran VERY HOT, and tried to overspeed. I only let it run for about 30 seconds before turning it off. No bother, I had better plans for this mower.
I bought my Sears Craftsman mower back in 2004 mostly for the Honda GCV160 engine it had. I knew the deck was only mediocre quality, but I wanted to try the Honda engine. It's really a super engine, but since my Honda HR215SXA (bought used in 2005) has such an excellent deck with a great commercial engine, I never used the Craftsman anymore.
I had initially thought about painting the Lawn-Boy a "gunmetal" grey, like the Craftsman. Sears calls it "Storm Grey". It's a pretty combination, with the silver aluminum of the engine and red/maroon engine shroud/fuel tank. But after cleaning up this L-B, the bright green was SO lustrous, and in such good shape under the dirt and grime that was on there, I couldn't stand to change the color.
So I took the Tecumseh off and put it on the workbench. The mounting bolt pattern is the same between the Honda and Tecumseh engine. Both engines are also "fixed throttle" engines, using only the governor for speed control, so there are no throttle cable issues. The operator presence bail (flywheel brake) connects to the engine in slightly different ways, but it still worked.
Comparing the engines side by side, they look close enough in dimension to be swappable.
The Honda's crankshaft is a bit shorter, but the Craftsman blade adaptor adds an inch or so of length, so the actual hanging "depth" of the two blades is essentially identical. The Honda's drive pulley uses a slightly thinner belt than the Lawn-Boy, but it works.
Here are some initial photos of the Honda engine test-fit on the 10330 deck.
The photograph above is standing in front of the deck, with the rear wheels at the top of the picture. The Honda engine uses the same three bolt holes as the Tecumseh did on the 10330 deck. The Honda block actually has a 4th mounting hole, but it was not used on the Craftsman mower. It is in the same general location as the hole in the 4:00 position on the 10330 deck as photographed above, but does not line up directly.
Because some aluminum thread material was lost from the Honda block when I removed the three mounting bolts, I went ahead and purchased (3) 5/16-18 x 2" cap bolts with locking washers and nuts to mount the Honda block to the L-B deck. The Honda and Tecumseh both used the same length/thread mounting bolt (3/8x16 x 1"). The 5/16" bolts are just thin enough to clear the threads in the engine block to use as thru-bolts.
And with the rest of the mower family...
I'll write about the other machines in a little bit.