The idea came to me while using the original design.

 https://www.printables.com/model/267500-joint-cigarette-doob-holder-for-4-joints

I traced the logo in onshape then added to the original lid

Add colour changes before the logo layer in the slicer of your choice. I had to print with PETG as they I didn't have the appropriate colours in PLA, so printed the first layers super slow to get the logo instead of a sticky blob.