No. Going as low as possible and staying as low as possible is the best for any lithium battery. Here a good source: Accubattery. Note how “battery University” is not a credible source, despite their name. Maybe they made people believe this in the first place.
And here a primary source for the most fragile LiPo cells. Look at figure 7. Even down to 1.2 V and the cells still reached 50 cycles until they were at 80 % remaining capacity. Not going below 2 V and it will be just fine.