This concept has been explored (and successfully accomplished) many times on this forum. The general consensus though, is that it's quite a pain in the rearend and is best avoided if a horizontal engine can be had. In order to do this, you'd need to-
*Fabricate a mounting plate to position the engine at 90*
*Machine or otherwise alter the PTO shaft to adapt to standard shaft size/type/keyway
*Fabricate a new intake manifold to re-orient the carb at 90*
*Fabricate an oil slinger (If you are using a 4-stroke)
Other things worth considering- Depending on engine design, you may have to alter fuel tank mounting. In addition, vertical lawnmower engines are produced with a very light flywheel. The blade acts as the remaining flywheel weight. Without the blade, you'll need to adopt a new starting technique to keep the engine from ripping the starter handle out of your hand. Some 4-stroke engines will also require you to alter the dipstick/oil fill tube, otherwise it may drool oil out in the new orientation, AND oil check/changes will require additional effort.