You are referring to an
Given to Noah in his hand,
After the flood, a dove returned an olive branch to Noah.
There with Plato as he taught,
Plato's Academy contained olive trees.
Not evil omens from lost land,
Nothing at the moment.
Since antiquity it could be bought.
Wikipedia: "As far back as 3000 BC, olives were grown commercially in Crete; they may have been the source of the wealth of the Minoan civilization."
A gesture that can make a friend
"To extend an olive branch is to make an offer of peace or to approach a foe in the spirit of conciliation."
And ancients would have lit
Olive oil was used as lamp/torch fuel long ago.
Holy at the Vatican
Rosary beads are often made from olive wood.
From the grove it's split.
Olive grove; splitting olives.
Some have tried to make it better,
It gets refined more and more,
Olive oils are refined for different uses/grades.
But further from the fruit,
The more it becomes impure.
The highest quality olive oil is the least refined.
'All lives' = 'olives => Olives always matter.
I despise olives.