^Yeah, that's the weird thing about her accent. You'd think she would sound like her parents.
Just an example, but I sound nothing
like my parents. I have been living in a different city for most of my life so I picked up the local accent, while my parents still speak with their native accents.
Troi's father might be American, and Lwaxana might speak with a "standard Betazed" accent (which would be most logically treated as an American accent in translation), while Troi might be speaking with a slightly different accent due to locality, associates, acquaintances, or just random happenstance.
Or Troi has a tiny speech impairment that sounds like a vaguely exotic accent.