That's not a very good excuse when Star Trek is set in the future but mostly uses real life present day language conventions. In real life, language would most certainly evolve to be significantly different centuries on. Star Trek doesn't work that way.Picard isn't serving in the British navy. He's serving in Starfleet. He's saying it the Starfleet way.
Wait, seriously? British sailors say it like Americans?The Royal navy don't say 'leftenant' anyway, that's an army/RAF thing. The way the word is pronounced is a service specific thing. Starfleet say 'lootenant' so Picard, a veteran of the service for several decades, does. No mystery.