The japanese make a feature of cracks in a process called 'Kintsugi'.
I'm sure that Hank
@leehljp would know about it. Not sure how much it is used on timber.
That is a process that I had not heard. I did know that there was a "glue" that was made from lacquer (Japanese lacquer which was quite different from USA lacquer.) I didn't 'notice' any kintsugi items on display during my time there, and if I did see some, I didn't know what I was seeing. That said, I did tour quite a few ceramic kilns over the years.
To STOP the wooden lid's crack from expanding, there are two ways:
1. Simple thin CA glue or 24 hour epoxy heated to about 90° or maybe 100° (I'm guessing) to make the viscosity more like water and drip it over the crack from both sides. The real work comes in when sanding after. Put it back onto the lathe and do a fine touch with a scraper to bring the wood-glue back smooth on both sides.
2. To accentuate the crack and also stop its spread, drill a 1/16" or 3/32" hole at the very end of the crack. Fill it with a peg that goes all the way through. A good contrasting color is sometime helpful aesthetically. Do NOT use a peg that has to be forced into the hole or it will open the crack.
Drilling a hole at the very end of a crack is a skillful way of stopping a crack from spreading. Done right, it can do to the object as the same purpose as "Kintsugi". Of course, after the drilling and inserting of a dowel, apply CA or epoxy to the crack and turn the excess off a few days later. Also, I wonder what gold or specific color added to epoxy would do to accentuate the crack. Sanding dust of the lid itself will cause a dark accentuation.
Many choices. The idea is being creative. Some work and surprise us

; some don't.
A link: https://www.google.com/search?
Also works on many different materials.