Why reduce the printing resolution? Why not let the printing software resize the image? All this assumes that you are printing yourself. If you are, note that the relevant setting is often "dpi", not "ppi", but it's ppi in the Lightroom print module. In general, the best results are obtained by setting this at the native resolution of the printer. I suspect that the results would be better than decreasing the resolution. And it's not like people will be pixel peeping, so I suspect the results will be more than adequate.
Another option instead of standard resizing (or to use first) if you use Adobe products is to start with "Super Resolution" in the enhance context menu. In my experience, it doesn't always help, but it sometimes helps quite a bit. I was recently sent a JPEG taken at a race that was only 147 KB (!) and asked if I could make 8 x 10 prints. Using super resolution, I was able to make entirely acceptable 8 x 10 prints--not something I would exhibit in a show, but good enough that the recipient was delighted with them and framed them.
I don't know if it's still up, but Smugmug used to have a page describing the practical minimum file sizes for various sizes of prints.
On the other hand, if you're sending this to a lab, none of this (including the ppi setting) matters because there is actually no ppi setting in an exported JPEG file. Many labs will simply tell you to send them the biggest file you can and let them deal with resizing. If you're doing that, I would see whether super resolution helps. if so, convert the results to JPEG and send that in. Otherwise, just send the largest JPEG you can--that is, export at maximum quality.
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