Yes, you need to know what your chamber neck diameter is. If you have access to the reamer print, it will show you. If not, measure several fired cases, as suggested, and add .001" for spring back and you will be close.
Not familiar with .338 Lapua brass, but that sounds thick. If all your brass is that thick and .369 is largest bushing, you have one option, that I can think of.
Use your largest bushing and then run a .336" mandrel to set your .002" tension. Remember that it is actually the amount of neck that is sized and not the bushing that determines your actual tension.
If it was mine, I would turn the necks for .004" overall clearance in the chamber neck, as J E recommended. If that is excessive vs chamber neck, at least turn to the thinnest side of your brass. FYI, the proper tools for neck turning can be expensive. The expander die and mandrel combo are a lot cheaper.