Partially out of need and also as a memorial to her, this evening I decided to reverse engineer some of her knots and see how it is done. It took a bit of effort, but after an hour or so of picking and prodding I was finally able to figure it out.
Seeing how much everybody here adores their Yixing teapots, I felt that maybe someone else would like to learn how to do it. Who knows, may be in the future it will save a few teapot lids from certain doom ;)
Despite its complex looks, the knot is quite simple.
Step 1: Loop your chosen thread between the handle and the lid nub as seen. You can use any colour thread but bright red is the classic way to do it. I'm using red nylon thread that is about 1mm thick.
Step 2: Loop around again until you get four strings in the center with two loose ends at each side.
At this point you might also want to adjust how much slack there are in the strings. If there is too little slack, the lid will be a lot more difficult to open, and in the worse case, you may not be able to close the lid at all.
Step 3: Begin by taking the loose end on the left. Lay it over the top of the middle threads and then under the right loose end as shown. Initially I found it easier to do this when I flipped the teapot over, but later on when I got better at it, it made less of a difference.
Step 4: Take the right loose end and wrap it under the middle threads. Then pull the end through the loop formed by the left loose end. Tighten. This is basically just a square knot. Once you get this first knot in, you may wish to recheck the amount of slack and readjust if necessary
Step 5: Now do the opposite. Take the right loose end, lay it over the top of the middle threads but under the left loose end. Then take the left loose end, wrap it under the middle threads and pull it through the loop formed by the right loose end.
Step 6: Repeat steps 3-5. This picture basically shows steps 3 and 4 repeated.
After several goes, the pattern begins to emerge.
You can stop at any time, but in this case since I ran out of un-frayed string, I had to end it. If possible, I probably would have repeated steps 3-5 an additional 2 times here.
Step 7: Snip off the loose ends and leave about half a centimetre of a stub. Note that there are many ways to end the knot, some more artistic or fancy, but I did it the simplest way.
Step 8: Now comes the scary part. You want to melt the frayed ends and harden the ends of the knot so that it will not fall apart. Don't burn the rest of the knot.
This is how it should look like if done properly. The black "button" of melted nylon will keep the knot tight and prevent the end from fraying. Now repeat for the other frayed end.