If you want strong AHAs (not that I would recommend strong ones for the lips), I use a 10% glycolic acid gel on my face and a 5% glycolic acid gel on my eyes -- the ingredients are few and it does the trick.
You can get, I think, up to 15% glycolic acid products (lotions, creams, gels) over the counter. 15% is a high percentage and I can't imagine wanting more than that for self-treatment on any part of the body.
For products that are made for the face (and products that are made for the body), check beauty.com (which is attached to, but has a different product selection than, drugstore.com) and dermstore.com for a pretty big selection of products - both sites sell quite a few dermatologist and specialty lines; I prefer the selection of dermstore but the prices of beauty.com, and there are some things you can only find on one of them so it pays to look at both if there is something you are interested in.
They both have free shipping after a certain $ amount, and often have coupon codes out there on the internet for even bigger deals.
Additionally, you can often get ostensibly-for-dermatologist-office-sales-only products from marketplace sellers on amazon.com, which is where I got my eye gel for a huge discount.
For a relatively high-AHA product intended just for the body, one example is a body lotion called AmLactin which is a "clinically proven alpha hydroxy therapy" with 12% lactic acid. I got it at CVS pharmacy for about $8, I think, and I had noticed that it was also available at drugstore.com, if I remember correctly.
I would not recommend products by "Alpha Hydroxy" (that's the brand name of the products) because I tried several in their line this summer and they all gave me a rash, acne, all sorts of trouble. It could have been just me, but I've never had an AHA product do that to me before, and the fact that 3 different products in their line, even the oil-free version, did that made me wonder what was going on. Many bricks-and-mortar stores have stopped carrying this line and you have to order it online.