Every single face has some asymmetry: one eye is bigger, one brow is higher, one side of the lip is thinner etc.
When pre drawing the shape of the lips, we certainly aim to create as much symmetry and balance as possible. Slight asymmetry can be fixed by adding a little bit on one side and/or removing a tiny bit on the other to create as much balance as possible.
BUT We must always stay within the natural lip border! We absolutely can not tattoo outside lip tissue as the skin there is different from the skin on lips: it has pores and hair, and tattooing in this area will not only result in having hairy and porous lips, but also the colour on facial skin will look different from the colour on lips.
Now about making the lips bigger. Very often, lip tissue is very pale right next to the vermilion border. In this case, by colouring in this pale bit the lips will indeed start looking plumper and fuller. But as with asymmetry, by no means we can go outside of the natural lip border.
Unfortunately there still are some "artists" around who tattoo outside the natural lip border, so please, if anyone tells you that they can make your lips bigger with permanent makeup, run away!
To summarize, very slight asymmetry can usually be corrected with permanent makeup, and if your natural lip border is pale, permanent lipstick may make your lips look fuller by giving the colour to the pale bits. But if you would like to achieved more dramatic effects of lip augmentation, or correct a more obvious asymmetry, you should seek help and advise from aesthetician doing lip fillers