Don't know how you can tell the crankshaft is moving laterally while it's running, but if true there's a very serious problem. You should not run it again until the issue with the bad bearing is resolved. Endplay (straight in/out) is normal to a very tiny fraction of measurement of the crankshaft. There should absolutely never be any lateral (up/down, side2side, etc.) play in the crankshaft.
The bearings must be replaced if there's lateral play in them, and of course the seals must be replaced at the same time. Get a full gasket set to seal the case back up, don't just squeeze on some gasket maker.
Note: Bearing failure might indicate the engine had been run very low on oil. Get the case set evenly horizontal and check the oil on the dipstick before you open the case, and look at the condition of the oil for being dirty or darkened. Refill with new oil no matter what.