Many designs are not created with laser cutting / engraving in mind, as shown here.
First, you need to decide what you want to fill, what you want to score and what you want to cut out. Move all the fill items to one layer, the score items to another and the cut to a third. That is all the layers you need, unless you want to do different fill effects in certain areas.
I personally use layer 00, Black for engrave, layer 01, Blue for score and layer 02, red for cutting. Many others follow this convention as well, but which layer you personally use for these is up to you.
Once you have those items moved to the appropriate layers you can begin tweaking them. If you set the layers to fill and use the scissor tool you can cut away the parts you don’t need and it will automatically close the shape. Make sure you are working in wireframe mode rather than filled rendering.
Nice about the trimming tool (I overlooked it, I was going to import in a CAD software)
So I have to do everything by hand.
Anther solution I thought about is changing the vector designs to two colours and then trace them in lightburn. It works very well when it is two colours, the problem is with 3
There are ways to do it using the boolean tools, but without knowing the exact results you require I cannot explain. The main thing with boolean tools is you can only work with 2 items or groups of items at one time and ther ecan not be any 3 way connections(T or Y type joints), only 2 lines can connect.. Use the boolean assistant to preview the operation before committing.