Give me insight to the best kind: lubricated or not: Some are supposed to be more sensitive than others. Provide your own or let the lady supply.

A professional always supplies..no need to worry.

they obviously want to make sure they are present at the scene of the crime but some ladies have certain brands that work for them...
(ie. issues with excessive contact with latex may cause a lady to provide a latex free condom...etc.)
I think most guys will tell you to bring your favorite on a date just in case she had a cover mishap!  Especially if you have a particular reason for needing a certain brand.
(On my last date we used my brand just because they were on the bedstand in my bedroom.)

Have your own and have a variety, with a couple options to choose from.  I can't imagine requests for non-lubricated.  The bottom line is prepare yourself, but wear whatever she would like you to, if she feels more comfortable making the choice.

My providers have been prepared but had no problem with allowing me to use my own.  I get far more out of an ultra-thin or a polyurethane and she'll get more out of a polyurethane too.  That is why I like to use my own.