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First, we are not "redefining" prayer. We are using the older and historic meaning of the word. I made that point in my last post with an observation on the shifting of the semantic field of the word "pray" over the past couple hundred years --- can you please deal with that?

There in may be the problem. Let's turn to the word prayer in the New Testament.

proseuchomai is the greek verb for pray.

4336 proseúxomai (from 4314 /prós, "towards, exchange" and 2172/euxomai, "to wish, pray") – properly, to exchange wishes; pray – literally, to interact with the Lord by switching human wishes (ideas) for His wishes as He imparts faith ("divine persuasion"). Accordingly, praying (4336/proseuxomai) is closely inter-connected with 4102 /pístis ("faith") in the NT. HELPS Word studies

Source? And I'm not sure this really deals with what we mean in English. For instance, it clearly does not apply to historic English usage.

From etymology online

pray (v.) early 13c., "ask earnestly, beg," also (c. 1300) "pray to a god or saint," from Old French preier "to pray" (c.900, Modern French prier), from Vulgar Latin *precare (also source of Italian pregare), from Latin precari "ask earnestly, beg, entreat," from *prex (plural preces, genitive precis) "prayer, request, entreaty," from PIE root *prek- "to ask, request, entreat" (cognates: Sanskrit prasna-, Avestan frashna- "question;" Old Church Slavonic prositi, Lithuanian prasyti "to ask, beg;" Old High German frahen, German fragen, Old English fricgan "to ask" a question).

That encompasses the wider meaning more accurately. In Shakespeare's "Comedy of Errors" (Act 2, Scene 2) when the character says to the man who struck him,

"I pray, sir, why am I beaten?"

he is not adoring the man, nor is he exchanging wishes with him. He is urgently asking him a question. That's all.

That illustrates a wider usage than your Greek lexicon suggests.