Forget about lapping. Lapping the sole of a plane, especially a jointer, is the fastest way to make the sole convex and likely make it worse than it was when you got it. By all means, you can go the old plane route, wooden or metal plane is your choice, but try it before you flatten it. It might not need to be flattened.
If you feel it does need flattening, I repeat, do not lap it. A much better way to proceed is to scrape or file the sole. When I used metal planes I filed. Now that I use wooden bodied planes I scrape instead.
All you need is a long straightedge, slightly longer than the sole of your plane. A long straight piece of wood will do just fine, no need for a machinist straightedge. Clamp the plane upside down in your bench vise and check it all over with the straightedge. Color the high spots with a pencil on a wooden plane or a Sharpie on a metal plane. Then scrape or file the marks away. Recheck with your straightedge, recolor the high areas, then file or scrape the high spots away. Wash rinse and repeat until the sole is as flat as you want it. I have used this method on metal and wooden planes with soles as long as my current 30” long jointer and in my experience it works far better than lapping.
But again, the best recommendation is to try it first. Not every plane needs to have its sole flattened. If it works fine, don’t fix what isn’t broke.