I took out my lip piercing out about two months ago after having it for about a year and a half..
The fistula hasn't shrunk or closed at all, not that I really expected it too.
Does anyone here think oil rubs would help it close up or shrink it ?
I don't mind a scar but I dislike like the look of the concave indent it has left.

Also would dermal punching the area and letting it heal create a less concave scar?

its only been two months just be patient 

the skin will return to a regular shade and hue in due time.  you'll more than likely be left with a slight indention which will be noticable if someone is staring at your face.  biopsy punching will not remove it, but will incur a larger scar if attempted.  vit e oil may speed up the process of becoming more regular in appearance, but it may also clog the pores on your face and make you break out.  leave it alone, you'll be fine.

I agree that you'll be fine.  I disagree that it will be only a slight indention over time.  Sounds to me like that baby is seasoned.  The fistula will shrink over time, but I'd imagine you'll always be able to put a narrow gauge piece of jewelry in. 

Dermal punching will not do what you want it to.  Perhaps a well trained practitioner in your area would be able to abrade the fistula for you...

A cream or liquid foundation will minimize the appearance of the mark if you must hide it.  You certainly wouldn't have to wear the makeup on your whole face, just on the area.  

I'd vote a definite NO to dermal punching if you want to minimize scarring. This is what it says about that type of scarring in my book, The Piercing Bible--The Definitive Guide to Safe Body Piercing:

Atrophic Scarring
Atrophic scarring, a depression or pitting below the normal skin level, sometimes occurs when a piercing migrates. Unfortunately, this type of scarring is usually permanent. Navel and facial piercings are the most common sites to find this type of pockmark. There are no easy fixes, but a dermatologist can explain treatments such as dermabrasion or laser resurfacing that might be effective. If the piercing can be maintained, generally the best way to deal with this problem is to leave jewelry in place. This will usually mask the scar or at least part of it.

...so the best way to get rid of visible scar tissue from a closed piercing is to put jewellery back in it to hide it?

Well. . . it won't "get rid of," but it certainly won't be as easy to notice the scar tissue if there is constantly something hiding it.

A scar is something you should have considered before the piercing. Any piercing can leave a scar.

full agreement, but it's counter logical.  she wants to remove the piercing and hide the scar tissue.  saying that the best way to hide the scar is to wear jewelery just doesn't make sense.

I will preface this by saying I know nothing of piercing scars but I do know acne scars: the best treatment I had for the reduction of my acne scars was derma-planing and chemical peels along with an at home microfoliant. My dermatologist did discuss biopsy punching a few of my deeper scars because the newer scars would respond better to the derma-planing and chemical peels. I never went that way though so I cannot comment on if it actually works...

good luck and I hope a pro can weigh in with a bit of info on derma-planing, in conjunction with the chemical peels it worked rather well. my skin is still not baby butt smooth but most people are shocked to learn I had horrifically acne scarred skin.