Three things I do to naturally plump up my lips. If you do them consistently you'll see results. It does not happen overnight, but it will help since they all increase circulation and blood flow to the area.
1. Massage your lips and the surrounding area nightly. This doesn't mean rub and tug; it's a gentle massage. You can sort of pluck/pinch your lips and the surrounding tissue to increase blood flow.
2. Exfoliate your lips weekly (at a minimum) with a nice sugar scrub. You can buy one or make one (just Google it for a million different recipes). I use the one by Suzanne Somers. It's natural/organic and I like it. This will keep your lips moist and keep lines away plus the extra manipulation helps blood flow to your lips.
3. Stretch them. Look at yourself in the mirror. I'll bet your lips are not only thinner, but shorter across? I find that when I massage them, I also take two finger and gently stretch them right above/below the lip line (towards the sides of my face). GENTLY is the keyword. This has helped them stay in their original shape and not turn into a little pucker.
Not even sort of natural. Way too full.
And here's the last thing: If you do go and get injections, please err on the side of natural to really look ageless. Nothing screams "I've had work done!" more than too-puffy lips (or cheeks for that matter).