You need to export to one of whatever various color profiles your print shop can use and embed the profile you actually designated in your export settings. The vast majority of print shops can handle sRGB, Adobe sRGB, and various CMYK based profiles. If they can handle Prophoto RGB (ROMM - Reference Output Medium Metric) then you can use that, too.

But in most cases it isn't really going to make much difference in the end. When you loaded the printer/ink/paper's color profile onto LR, LR limited itself to only using the colors that the profile said that particular printer/ink/paper combination is capable of reproducing. If all of those colors fall within sRGB then there will be very little, if any, difference in using a wider colorspace to export the image. If all of those colors fall within Adobe RGB then there will be very little, if any, difference in using a wider color space than Adobe RGB to export the image.

In fact, depending on the contents of the image, you could have smoother transitions for tones and hues by using the smaller colorspace, which has less 'distance' between each discrete value at the same bit-depth than a larger color space will have. Theoretically, your best result would be to use the smallest color space that includes all of the colors the printer/ink/paper profile allows.

The other question you must answer is what colorspace your monitor is using. Just because LR uses ROMM internally does not mean you are seeing the image on your monitor in ROMM. If your monitor is a standard sRGB (or Adobe RGB) monitor, the internal ROMM image is already being translated into sRGB (or Adobe RGB) before you're seeing it as you are editing.

We can all view the following CIE 1931 chart showing the Prophoto RGB (ROMM) color space on whatever monitor we are using. But if the monitor is not capable of showing the full gamut of ROMM colors, the colors we're seeing on the chart are not the actual colors at each location within ROMM. Even if we did have a monitor capable of displaying ROMM, if the chart was saved and properly tagged in sRGB, all of the colors displayed are going to fall within the sRGB color space. The differences between colors within the sRGB space and those outside the sRGB space are simulated. All of the colors displayed actually fall inside sRGB.