After Tata give you the Heroes badge and you have fetch the masamune part from the frog and you have to return to 1000AD again it's a good spot to engage Lavos again for this ending.
if you haven't figured it out yet all ending are so much easier to take on new game+ and after you beat Lavos first shape and you go into the shell. You can exit and save and continue the story and when you return you don't have to deal with the first shape. So you simply go out save, enter and beat the last two shapes, reload the save spot before the fight and move the story ahead for the next ending, enter and you only have to beat the last two shapes each ending instead of all three.