Save to Camera Roll with the Maximum available option will give you a jpeg with the full pixel resolution of the original. With this option you will end up with a file that is actually larger than you need.
Photoshop Mix allows you to create a custom canvas. You could create a canvas at the dimensions you need, then place the photo from Lightroom and scale it to fit the canvas. Then save the file from Mix to your camera roll. I understand that this is way more steps than you want, but right now I don't see a way to export from Lightroom mobile at a specific size.
Whomever you are sending the images too may be specifying the 300ppi requirement, but the truth is that the file size is determined by total number of pixels, not by resolution. If the file is the correct total pixel count at 72ppi it will print over 3x times larger than the same image at 300ppi. BUT the final output size can be set when printing so it really isn’t a relative requirement.