LightBurn has a similar tool in appearance but one that works and behaves functionally differently. In node edit mode you can “trim” lines up to an intersection by hovering over the line and hitting the ‘t’ key. The difference in behavior to what you’re describing here is that the resulting shapes are not automatically rejoined and will not necessarily result in a closed shape. Meaning there could be gaps between the trimmed line and any intersecting line.
There was actually a topic I created recently on this point you can read here:
Edit Node - Trim behavior - LightBurn Software - LightBurn Software Forum
You can still use this tool and adjust nodes accordingly to close gaps.
The preferred method for creating objects that result in a closed path is to use the Boolean tools+weld in various combinations. However, I’ve noticed that certain techniques that might work in other tools don’t result in the same output in LightBurn so you’ll need to readjust to the nuances.