I personally don’t have an inner lip but when I was studying tattoos and tattoo culture many ppl I spoke with all stated the same issues from theirs;

The inside lip has softer tissue so that the pigment of the ink tends to blowout much easier leaving the tattoo looking blurred and messy.

It fades very quickly as tissues get a lot more damage from eating brushing etc.

They can be very prone to infection due to amount of bacteria in the mouth.

They hurt like a bastard for a so/so tattoo.

That said it is on the inside and if you really want one get it done but personally I think not worth the effort required to maintain.

Take care
Matthew