There's no such thing as too much lube, lol!  As long as you are very clean and make sure you are fresh smelling, no provider should be daunted by you being uncut or by the amount of lube that is necessary.

There is a warning that using lube on the inside of a condom will compromise the integrity of the condom, but I've never found this to be the case.  I use quality condoms that can stand some lube on the inside of them(tested them with water, LOL).

appropriate lube on the foreskin area only underneath the condom

then enough lube (either / or / both natural vs out of a bottle) to allow penetration without discomfort

IT is amazing to me how many providers, even experienced ladies, have no clue about dealing with uncut cocks - and I'm talking condoms, lube and BBBJ....  sometimes you simply have to have a discussion with them about what works for you...

First, condoms need to fit with a tiny bit of movement.  (Friction is movement + pressure)  Too little movement inside puts all the friction outside.  
You may need to check the various styles & shaping.  Condoms also need to be tight enough on the shaft to stay on.
You might need to bring your own condoms but she will surely want to inspect the sealed packaging.  Some ladies will not use yours & I respect their right to decline but I've never been refused my respectful suggestion.
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None of the providers I've seen have put lube on the inside. Is that something that will help both cut and uncut guys, or do they not do it because most guys they see are cut and it's not needed for them?

I'm uncut and wouldn't have it any other way, and my biggest problem with condoms is that the minute I put one on it feels like my dick has been chopped off. I don't think that has anything to do with being uncut, and I don't think the lube will help with that initial shock. If I get going quickly I can keep it erect and pop, and it's not too bad even without the lube. The lube sounds like it could make things even better though.