Here's my thinking rodwha. Lyman barrels are 15/16" across the flats, which is .9375. If it's bored out to .615, the barrel walls will be .16125. That's just a tad bit thicker than the barrel wall at the muzzle of my Omega X7 (which has the QLA cut off). Given that shotgun loads achieve a much lower pressure than do ball or bullet loads I think it would probably be safe with modest loads. But I don't think I would shoot heavy charges from it, and certainly not balls.

I think your problem would be finding a smith willing to bore a 15/16 barrel out that big.

Another problem might be the breech plug. Most ML rifle barrel breech plugs are 5/8-18, which is tapped into a 37/64 hole (0.578). Boring the entire barrel through for 20 GA would remove the plug threads, so the boring would need to stop short of the threads, or a larger diameter plug would be required.

Now all of the above is my pure speculation. I recommend you seek a professional opinion from one of the barrel makers listed in the HNI Black Powder Reference Forum via a telephone call or e-mail.