While any may work, not any is good for a phone. e.g. you don't want a lanyard that has metal parts as that can scratch the phone, especially the screen. The advantage of the official Nokia one is that it is all leather put together with string and no metal parts that may scratch your phone.
I just ran into this issue as well - both my wife's and my lanyards for the 1020 started to fray at the same time a month back, and mine just completely fell apart into two separate loops today. After researching for a stupid amount of time (is it really that hard to make a nice-looking metal-free lanyard?), I found this on eBay. Ordered two tonight... here's hoping.