RPI3 - Onboard PSU 230VAC to 12/5VDC?
It could be death-courtlingly dangerous. Also, mains to d.c. PSUs are not simple to design. There are a lot of things to consider including creepage and clearance rules and plenty to learn about.

If you were to do it, you'd need to mount the whole system in box that humans can't touch, ensure that the mains voltages have appropriate clearances from the RPi GPIO pins and make it very robust. 

You can get very neat little PCB mount mains to 12V modules these days, but they are low power and almost definitely not enough for what you want. 

I would be more tempted to use a 5V step-up to 12V d.c. to d.c converter if the LED power budget was modest enough (or even better use Maz's idea below!).