English
eldership
From elder + -ship.
Formed from elder + -ship
Proto-Indo-European *h₂el- ‘to grow, nourish’
Proto-Indo-European *h₂eltós
Proto-Germanic *aldaz ‘old, grown up’
Old English eldra
Middle English eldre
English elder
The story
The Lithuanian sense is a calque of Lithuanian seniūnija.
Today it means
noun The position of being elder or senior; seniority, precedence of birth, primogeniture.
Language periods are conventional ranges, not dates for this word.
Etymograph / eldership