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If you upres a file from 24'dpi to 36'dpi and increase the print size in the export menu, does lightroom perform the necessary adjustments as far as interpolation and sharpness.
I'm waiting to hear some "pros" answer this. But, IMO, the answer to your question is yes and maybe. Yes LR does some interpolation and sharpening(if you have it set), and maybe it's the necessary amount. That depends on your tastes.
When you enter a resolution, Lightroom will use an adaptive bicubic algorithm to resize the image for print. The sharpening settings you choose apply to the print output size.