Can you pierce through scarred lip tissue?

You could but why would you want to? Look if you are one of those folks who had a piercing and took it out for what ever reason, now you want it back beprepared. Piercing through closed piercings will generate even more damage and will leave a bigger scar than what you have now.

You need to decide before you get the piercing that once you get it, you will leave it alone and keep it. Piercings are not something you can take out and get redone at a whim, there is a price to pay for doing that, it may not happen now but down the road you will pay for your indecision. Scar tissue occurs when you cut tissue and let it close, piercings on the other hand are NOT scar tissue.

So before you opt to get anything repierced have the professional body piercer you are seeing check to ensure the piercing is actually closed by probing the piercing with a fine gauge insertion taper. If the piercing is still there but has shrunk then gently stretch the piercing back open (use a smaller gauge jewellery piece if need be till the piercing settles back down).

This will save you the healing time and further concerns later in life when you actually do remove the jewellery permanently. I am of course assuming you are getting your piercing looked at by a professional body piercer and not attempting to do this yourself (which would be a wrong move regardless of what I am telling you).