I create a box and convert it to path. Then I’d like to draw a series of line segments starting at one corner and ending at another corner … but I want the ends of the lines I’ve drawn to be joined to the corners.

How do I join a line segment to a node on a closed path?

Did you create a box as a rectangle, and if so did you convert it to a path first?

But, aside from that, it looks like LB only supports vertices with one or two vectors, but no more. It will simply make a third vector that can snap to it when laid, but grabbing and moving the vertex will only drag the first 2 vectors with it, not a third.

If you make a triangle as a closed path, add two more sides to make it like a rectangle with a single slash from opposing corners, because of that order of creation you have a triangle and two vectors with one common vertex and two points that aren’t tied to the triangle’s vertices, just coincident.

Then if you delete the slash so even though it’s literally just a rectangle, it will actually be two unrelated sets of 3 vertices and 2 vectors unless you do Auto-Join.

Looks to be by design? Two vector limits for any single point?

Yes, that was a lesson learned long ago.
I too have concluded there’s a two vector limit for any point.
It’d be nice have more if you’re using vectors to trace an object in LB.