Petroleum jelly/petrolatum/white petrolatum/soft paraffin or whatever else wikipedia calls it. Vaseline. Brands made no difference to me. It was all good. The one I got at first was Purol.

You mentioned a Beiersdorf product - was itLabello? Those classic dark blue tubes were most effective for me but I still went through massive amounts of it. The habit/addiction lasted for a few years, I found myself having to reapply thick coats of the stuff every 10 to 15 minutes - if I didn't, my lips would start to tingle, then burn, then flake and I'd become super unpleasant to be around. Over the years I tried several brands of lip balm, some more expensive than others. I'd say even say that the fancier, more expensive ones were the least effective for me, so I kept using Labello. One day I ran out (I literally used carry at least 2 tubes on me at any given moment), so I tried to get my usual go-to brand at the store -- but they ran out. Desperate and jonesing for another slippery fix, after not having slathered my mouth for several hours now, I got some Purol (petroleum jelly goop), just to get my grease fix. I immediately applied it after paying for it and didn't feel a need to reapply until a day or two had passed - no tingles, no burns, no cracks or flakes, no, dryness, no tightness. Nothing. I wasn't aware of my lips for that day and the next.

Eventually I found myself applying the stuff even less. About once every two days at first, then once a week, sometimes not at all for months at the time. I haven't touched the stuff in 3 or 4 months now, simply didn't need to. I do douse myself in baby oil after showering in the morning and evening, including my lips, and usually that's about all I require to keep my lips feeling comfortable. Sweet, sweet petroleum jelly/vaselines; they worked really well for me.