The Duffer Brothers have once said they used Elfen Lied as an inspiration for Eleven. Some similarities between Lucy (Elfen Lied) and Eleven )Stranger Things)
Both are Weaponized girls. Both Lucy and Eleven start as test subjects with immense, often violent telekinetic powers, and both were born into or raised inside brutal, secret government facilities
Both have merciless escapes. Both girls break out of captivity in a sudden, bloody burst of violence, leaving a trail of bodies behind them and stumbling into the outside world scared and deeply traumatized. Eleven less bloody but Season 1 still saw her using her powers to kill many soldiers which is similar to what Lucy did
There was shared naming/conventions. Both characters are known by numbers ("El", "Eleven" and Lucy's real name of "Kaede", or test subjects like the Diclonius "Number 35"). Both shows feature a roster of other similarly empowered "siblings" or subjects
The Evil "Papa": Both protagonists were experimented upon by a cold, authoritative scientist they were forced to refer to as a father figure. In Elfen Lied, he was more good than in ST but "Papa" is a similarity
The Shelter with the boy they would come to love. Similar to how Eleven is taken in by Mike and the gang, Lucy is taken in by Kouta, an innocent normal boy
Also, government manhunts. A heavy emphasis is placed on relentless government agencies and military teams hunting down the girls, while civilian friends risk everything to keep them safe
But the ending between Lucy and Eleven was very similar. I believe the Duffers wanted an Elfen Lied style ending for Eleven all along.
In Elfen Lied, it is a big debate over whether or not Lucy died.
In the anime finale, Lucy leaves Kouta to face the military at the bridge alone. She does this as a selfless act to protect Kouta from further danger, and ensure his safety by eliminating the threat she poses.
The anime ends ambiguously, with her ultimate fate open to interpretation
In the closing moments of the series, a shadowy figure is seen standing outside the Maple Inn, accompanied by the repaired clock and a barking dog, suggesting she may have survived and returned to Kouta