You're getting killed unfairly and unnecessarily by a lot of commenters who aren't half as deep as they want to make themselves out to be. Your preference is a bit different from theirs, so they feel justified in trying to make you out to be a jerk, when you most certainly aren't.
I did see this device on Amazon (https://www.amazon.com/BoSidin-Painless-Permanent-Removal-Epilation/dp/B083WDVSYY/ref=sr_1_2_sspa?_encoding=UTF8&c=ts&dchild=1&keywords=Hair+Removal+Epilators&qid=1606289709&refinements=p_72%3A1248873011%2Cp_36%3A1253954011&...) that may help her to find a more lasting solution to the lip hairs that pop up. While expensive, it has plenty of incredibly reviews.
Outside of that, I don't have any solutions, because I find myself sometimes in the same conundrum. I did want to comment to provide moral support. You've been remarkably patient with people who have some insane need to paint you as a bad person for having preferences and trying to gently work towards a solution. I commend you. I hope that you've been able to help her address the issue.
I would bet that it does. You could try talking whomever does your laser into going back over it? Bargain with a spot test maybe? I go over my lower legs, where my KP is worst, like 5 times. But I really don't even think about it taking longer, it's a non-issue. This is the one I recommend if you want to buy one some day:
BoSidin permanent hair removal device https://www.amazon.com/dp/B083WDVSYY/ref=cm_sw_r_cp_apa_i_9X.gFbX0DCYQJ
I’ve heard great things about the BoSidin device but it’s $339 with an $80 coupon on amazon. It’s still pricey but idk if it’s worth it. Me and my boyfriend are looking for the best hair removal methods.
BoSidin Painless Permanent Hair Removal Device, Epilation for Women & Men - Body and Face
https://www.amazon.com/dp/B083WDVSYY/ref=cm_sw_r_cp_api_i_FoHeFbETNHK28
I got one from Bosidin off of Amazon but I didn't do a whole lot of research beyond one or two reviews. Overall I'm happy with it.
You can get a good laser for at-home treatments for a few hundred dollars (mine: https://www.amazon.com/BoSidin-Painless-Permanent-Removal-Epilation/dp/B083WDVSYY). It takes a lot of work and time, but monetarily, it's hardly cost-prohibitive compared to professional work. However, you'll be limited to light skin areas with dark hair, and multiple sessions will be needed.
Alternatively, you could build an electrolyzer if you're technically skilled enough, or engaged/intelligent/desperate enough to learn electronic theory to build and test it, like this person did: https://hackaday.com/2018/05/01/hair-today-gone-tomorrow-via-electrolysis/. I'm still building mine to supplement the laser, but I designed my own version from scratch to be portable, since the electronics aren't too complicated and it's battery powered anyway. However, a purely DC system means that you'll kill the follicles by galvanization rather than pyrolysis, and although that means it's only needed once per follicle, it'll take about 90 seconds (ish) to kill each follicle, rather than only a few for an AC system. Still, it was like $50 of parts with plenty left over, so no complaints here.
Now, if those are not options, there is another option that I do not recommend. I've personally been hard waxing my facial hair off with good results. HOWEVER, this can lead to scarring and other problems if your skin can't handle it, and if you're on HRT and your skin has started to soften, you're going to have a bad time. Also it's not permanent and you need to grow it out each time to wax it off. And it's extremely painful, but that's honestly the least limiting factor.
As long as your facial hair is dark enough and your skin is light enough for the laser to work, just drop a few hundred on a good at-home laser (do not buy a cheap one if you're not just removing some peach fuzz on your lip). And if that's still too much, share the laser and the cost with friends and family if you need to.
Here ya go! It’s a bit pricey but I’d tou get it when it’s on sale it’s definitely worth it!
https://www.amazon.com/BoSidin-Painless-Permanent-Removal-Epilation/dp/B083WDVSYY
May be you can try Bosidin. Use the latest generation of Optimal Pulse Technology (OPT) of both laser and IPL hair removal technology.There are two sales channels, Amazon and official website.
https://bosidinofficial.com/
https://www.amazon.com/gp/product/B083WDVSYY/ref=ask\_ql\_qh\_dp\_hza