That seems like it could be maybe a cultural thing, or maybe even how the same word can convey a very different feeling in another accent.
If someone pronounces Lady as “lāh dih” instead of “lay dee”, the former feels odd compared to the latter, at least to me anyway.
And then there’s also probably a stigma associated with the time period and circumstances in which a woman was referred to as a lady, which may also make it sound off when used today.
I think referring to women as females is far ruder though personally, “Female” feels like “an individual that is not a male”, but Lady feels more like “A woman” with more pizzazz, if we ignore its past connotations