Probably a modern invented name shaped from names like Liesel or Lisette with a decorative ending.
Liserly is probably a modern invented name shaped from forms like Liesel or Lisette with a decorative ending. That kind of construction gives it a faint European flavor even when the exact lineage is unclear.
It sounds as though it belongs to the family of names that began as nicknames or diminutives and then stretched into something more stylized. Liserly feels ornate in a soft way. It has a lyrical flow that makes it seem delicate and somewhat old-fashioned, even though the form itself is contemporary.
The name sits between familiarity and invention, which is often where the most memorable modern names live. It has enough structure to feel elegant, but enough novelty to remain distinctive.