Well I think the Masamune being stolen in 1005 AD would have to do with the stuff happening in Cross.

And actually depending oh how you fight Lavos in trigger would determine how the time fields are effected.

If you go on the black Omen in 12000 AD and defeat Queen Zeal and fight Lavos or in 1999 AD and sucessfully kill it then you've succedded in killing Lavos befroe it has done any real damage.