Been there done that Check out some of the projects at my blog. The Mini has a 24V power supply that has lots of extra juice to offer. I tapped off the 24V, dropped it to 12V using a switching regulator. It powers the an arduino fan/temp monitor unit + fan. There is still plenty to spare. I suggest you also check the documentation at LulzBot http://download.lulzbot.com/Mini/ - you will find the specs for the power supply. It should also be able to support the power demands from an RPI (5V and < 1A).
Something to note. I have my RPi Octoprint server on separate power. I find I have to power on the Mini first before OctoPrint or sometimes I get a flaky connection to the RAMBO board. I think the RAMBO board needs a bit of time to boot up. If you power it all from the Mini, you may want to find a way to delay the startup of the RPi.