the situation you have is similar to many people trying to preserve their family heirloom vintage rolex. replacing a major component like the case is basically changing watches, not preserving grandpa's watch. your lugs look typical of what happened to vintage watches years go...someone adapted the lugs to fit a strap.
once you get the movement removed, rest the inner half of the lug against a sharp wooden edge and gently tap the outer part of the lug with a small wooden or plastic hammer to bring the lug back into position. gentle is the key. it's easier to control gently taps than attempting to bend the lug with wrapped pliers, as constant pressure is too difficult to maintain and that is how lugs are snapped off.
if things go wrong then bring the case and whatever broke off to an expert goldsmith, as they can reshape and use pure 14k gold to solder things back together. I don't know where you are located, but in Manhattan's jewelry district there are jewelry repair experts that could fix that case/lugs up very reasonably so at least it's the same watch your grandpa wore. Replacing the case should be a radical last-ditch solution.
