Images exported from lightroom are usually encoded relative to a particular displays characteristics and viewing environment (primaries, EOTF, surround, etc.).
sRGB is a specification of a "typical" desktop computer monitor.
P3 is an encoding used in digital digital cinema and has the ability to encode more saturated colors than can be encoded in sRGB.
RAW images can easily be encoded as sRGB or P3. The key, however, is that the images should be encoded based on the capabilities of the display on which you plan to view those images. If you encode the image as P3 but then view those images of a sRGB monitor, they will look incorrect. And vise versa, if you encode as sRGB and view the images of a P3 monitor, they will also look incorrect.
Color management can help reconcile mismatches. For instance, if you send a P3 encoded images to an sRGB display, it's tagged correctly, and there's a color management system in place, the images will be converted to sRGB before being displayed. However, in that case the display is physically incapable of displaying the most saturated colors specified by the P3 encoding. The color management system will remap that color to a color within the sRGB gamut. If you send a sRGB image to a P3 display, it's tagged correctly, and there's a color management system in place, the image will look exactly as it would have on an sRGB display, but won't take advantage of the display's larger color gamut.
In many software systems (including many printer drivers), if the images aren't tagged, or there is no color management, the images will likely be assumed to be sRGB.
Long story short, the choice of how you encoding should be made based on the intended usage. If you know the display it will be viewed is a P3 display, encode as P3. If it is sRGB, encode as sRGB. When in doubt, sRGB is probably safer.