It's definitely not just cumulative 250 lines. Everybody would have heard 250 lines from the 4th palace up to the final boss fight. But there are many which did not.
I am pretty sure it's either 250 cumulative lines, BUT not every line-type does count or some equal lines do count as unique (like baton pass from Ann to Morgana is a different line system based as Morgana to Ann)
But honestly, for everyone who is farming for it: Just and trigger things you did not did already. Explore the palaces and mementod as much as possible, don't run away, always try to trigger new lines. And if not possible, trigger at least some lines, because as you see, most people got it with leas then 250 unique ones so there has to be a reason.
It's not that hard. I got it in Mementos just after the fourth palace.