Per the Lich's Soul Sacrifice description, both the body and soul of the imprisonment spell's target are trapped inside the phylactery. The description also states that this imprisoned "creature" is destroyed in 24 hours.
the lich uses the [imprisonment] spell to magically trap the target's body and soul inside its phylactery.... A creature imprisoned in the phylactery for 24 hours is consumed and destroyed utterly, whereupon nothing short of divine intervention can restore it to life.
p. 203 DMG 5e (emphasis mine)
If we are to interpret the term "creature" as referring to both the body and soul of the imprisoned entity, then the soul is destroyed utterly.
If the soul no longer exists, does it have any afterlife experience?
Might a person voluntarily offer their soul to a lich to avoid judgment for their False or Faithless soul?
The last bit of the Soul Sacrifice description does state that divine intervention can restore a destroyed creature to life, so it likely would not be outside of the power of Kelemvor to recover a soul attempting to avoid his judgment.