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What modelling program do you use to model your container?
I used Fusion360 which makes it very easy to create threads into things. I just created the same thread in both container and lid. One carved into the model and the other added to the model. I did not do anything special beside that. Even not give it extra space for tollerance. Fusion360 handels that pretty well.
What could make problems (and that would be the same to any model which needs a precise fit like holes for rods, screws etc.) is, that depending on the slicer you use and the diameter of your nozzle etc. there can be a difference where plastic is extruded. ON the line or OUTSIDE the line. A nozzle printing of 0,4mm width printing a circle ON the line would make the circle 2x 0,2 = 0,4mm smaller. Most slicers should consider this and also do correct it. But under certain circumstances it doesn't.
I know nothing about your model, but maybe this helped a bit if I did not misunderstood.