As far as I am aware, LXX uses a word in this crucial verse which would uncontroversially be translated as "pierced" into English. If it predates the Roman practice of crucifixion and/or Jesus's death in particular, this is very significant information to my mind.
I would also like to know, if we do not have a pre-Christian fragment of Psalm 22:16 from LXX, what is the scholarly consensus about faithful preservation of LXX, and this verse in particular.
I do not know the answer to the OP's question. However, according to the list provided in https://en.wikipedia.org/wiki/List_of_the_Dead_Sea_Scrolls we have among the Dead Sea Scrolls (DSS) document "4Q88" containing Ps 22:14-17 which is dated in the Hasmonean period.
It was found in Cave #4 and dated to about 100 BC (the middle of the Hasmonean period).
Numerous other copies of the psalms among the DSS were also found but as far as I can work out (others may have better information) this is the only document contain the verse Ps 22:16.
