If the "dither" option is set in Photoshop->edit->Color settings then your 16 bit prints will be dithered when printed with an 8 bit driver. Even when printing through a null transform. With it off they will not be dithered. I don't know what LightRoom does.
Printers have to dither just to print 8 bit images since they only have 8 or 10 inks to work with to create 16M different possible colors over a very small area. Just turning on the dither option eliminates any advantage 16 bit driver paths provide which is mostly theoretical in any case.
This has got me confused (I'm not very tech-minded). You're saying that to enable a 16 bit printing workflow, the Photoshop Colour Settings dither checkbox must be switched off? As it is not in any of the print dialogs, it is an easy thing to overlook. I've always assumed that for day-to-day colour space conversions (e.g. converting AdobeRGB images to sRGB for a client) it should be switched on (to avoid banding). I'm not confident that I can remember to toggle this setting on/off depending on whether I'm printing or converting files for clients.
I've been doing some further tests, printing some gradients (white to mid grey) with my normal print workflow (i.e. with a print profile (in this case, the Epson 3880's canned profile for Semigloss), 2880 dpi, high speed off).
I made 4 prints, all of the same 16 bit file (i.e. I'm not converting the file in Photoshop to 8 bit for the 8 bit tests - I'm just unchecking the 16 bit checkboxes in the Epson dialogs.)
1) Epson 16 bit. Photoshop Colour Setting = no dither
2) Epson 16 bit. Photoshop Colour Setting = dither
3) Epson 8 bit. Photoshop Colour Setting = no dither
4) Epson 8 bit. Photoshop Colour Setting = dither
They all look the same, with smooth gradients, except for (3) which shows some slight banding.