The best would be to test it : take a good & sharp image, make a virtual copy and crop it extensively to an area of interest to be able to print patches of reasonable size even at lower resolutions. For each resolution (180, 150, 120, 90dpi) make one print resampled in the driver, another resampled in LR, and look.
I'm sorry not to be HP-specific, but here are my findings with my Epson R1800 and Lightroom :
- I don't see any quality issue before print resolution goes under 150-200dpi, so all the following only applies to resolutions under 150dpi,
- The Epson driver does a nearest-neighbour interpolation leading to discernable square pixels (ouch),
- Lightroom does a very decent job of uprezzing, I'd think it's something like bicubic (perhaps with some mild sharpening?).
Keep in mind that uprezzing is creating information from (almost) nothing, so don't hope for magical results.
So, if your print resolution is above 150 or 200dpi (please test as your mileage may vary), just send that data without resampling in LR.
If it falls below that threshold AND you found the driver doesn't interpolate properly, resample in LR by checking the appropriate checkbox above the profile.
You may set the resampled resolution to 300dpi as it should be the "native resolution" of an HP driver but for one I'm not sure of that, for two I'd doubt that any significant differences would show with the default 240dpi setting.